Coatings Technology Handbook 2010 Part 2 doc

4-6 Coatings Technology Handbook, Third Edition (4.13) where G e is given by Equation 4.11 and f e is a probability factor for trapped entanglements. In the case of network imperfections, Equation 4.12 is modified. 14,15 The quantity f e can be calculated if the reaction parameters for network formation are known. 14,16,17 4.3.3 Other Properties Several other properties of dried films influence performance characteristics. Examples are the coefficient of thermal expansion, ultimate mechanical properties, stress relaxation and creep, and dielectric prop- erties. However, correlation of these properties with structure for polymeric films is not well established; some of the more successful attempts are treated in Refs. 2 and 3. References 1. R. B. Bird, R. C. Armstrong, and O. Hassager, Dynamics of Polymeric Fluids, Vol. 2. New York: Wiley-Interscience, 1987. 2. J. D. Ferry, Viscoelastic Properties of Polymers. New York: Wiley, 1980. 3. D. W. Van Krevelen, Properties of Polymers. New York: Elsevier, 1976. 4. 5. J. W. Berge and J. D. Ferry, J. Colloid Sci., 12, 400 (1957). 6. G. Pezzin and N. Gligo, J. Appl. Polym. Sci., 10, 1 (1966). 7. Ref. 2, p. 510. 8. T. Matsumoto, O. Yamamoto, and S. Onogi, J. Rheol., 24, 279 (1980). 9. D. W. Meitz, Ph.D. thesis, Carnegie-Mellon University, December 1984. 10. Ref. 3, p. 383. 11. F. Bueche, Physical Properties of Polymers. New York: Wiley, 1962. 12. Ref. 3, p. 384. 13. Ref. 3, p. 266. 14. E. M. Valles and C. W. Macosko, Macromolecules, 12, 673 (1979). 15. P. J. Flory, Principles of Polymer Chemistry. Ithaca, NY: Cornell University Press, 1953, p. 458. 16. M. Gottlieb, C. W. Macosko, G. S. Benjamin, K. O. Meyers, and E. W. Merill, Macromolecules, 14, 1039 (1981). 17. D. S. Pearson and W. W. Graessley, Macromolecules, 13, 1001 (1980). G M fG RT c ee  ρ + DK4036_C004.fm Page 6 Thursday, May 12, 2005 9:39 AM © 2006 by Taylor & Francis Group, LLC Ref. 2, see discussion in Chapter 17. 5 -1 5 The Theory of Adhesion 5.1 Contact Angle Equilibrium 5- 1 5.2 Forces of Attraction 5- 3 5.3 Real and Ideal Adhesive Bond Strengths 5- 8 References 5- 9 When pressure-sensitive adhesive is applied to a smooth surface, it sticks immediately. The application pressure can be very slight, not more than the pressure due to the weight of the tape itself. The adhesive is said to “wet” the surface, and, indeed, if the tape is applied to clear glass and one views the attached area through the glass, it is found that in certain areas the adhesive–glass interface looks like a liquid–glass interface. From this one would infer that a pressure-sensitive adhesive, even though it is a soft, highly compliant solid, also has liquidlike characteristics. Some knowledge of the interaction between liquids and solids is beneficial to the understanding of adhesion. 5.1 Contact Angle Equilibrium When a drop of liquid is placed on a surface of a solid that is smooth, planar, and level, the liquid either spreads out to a thin surface film, or it forms a sessile droplet on the surface. The droplet has a finite between the solid and the liquid and the surface tension of the liquid. The contact angle equilibrium has received a great deal of attention, principally because it is perhaps the simplest direct experimental approach to the thermodynamic work of adhesion. Many years ago Young 1 proposed that the contact angle represents the vectorial balance of three tensors, the surface tension of the solid in air ( γ sa ), the surface tension of the liquid in equilibrium with the vapor ( γ lv ), and the interfacial tension between the solid and the liquid ( γ sl ), The force balance can be written γ sa = γ lv cos ++ γ sl (5.1) Young’s equation has come under criticism on the grounds that the surface tension of a solid is ill defined, but most surface chemists find his equation acceptable on theoretical grounds. The equation can be written as a force equilibrium or as an energy equilibrium, because the surface tension, expressed as a force per unit of length, will require an energy expenditure of the same numerical value when it acts to generate a unit area of new surface. Harkins and Livingston 2 recognized that Young’s equation must be corrected when the exposed surface of the solid carries an adsorbed film of the liquid’s vapor. The solid–“air-plus-vapor” tensor, γ sv , is less than the solid–air tensor, γ sa . Harkins and Livingston introduced a term, π e , to indicate the reduction thus: γ sv = γ sa − π e (5.2) Carl A. Dahlquist 3M Company DK4036_book.fm Page 1 Monday, April 25, 2005 12:18 PM © 2006 by Taylor & Francis Group, LLC angle of contact (Figure 5.1). The magnitude of the contact angle depends on the force of attraction 5 -4 Coatings Technology Handbook, Third Edition where r is the center-to-center distance between the dipoles. If the rotational energy is less than the thermal energy of the system, then where k is Boltzmann’s constant (0.0821 1·atm/mol deg), and T is absolute temperature (K). There may be dipole-induced dipoles, where the potential energy of interaction is given by where α 2 and α 1 are the molecular polarizabilities. There may be acid–base interactions 7,8 across the interface that can lead to strong bonding. Examples are hydrogen bonding, Lewis acid–base interactions, and Brønsted-type acid–base interactions. Covalent bonding between adhesive and adherend, if achievable either by chemical reactions or by high energy radiation, can lead to very strong bonds. Interdiffusion, usually not achievable except between selected polymers, can also lead to high adhesion. The force of attraction between planar surfaces has been derived from quantum mechanical consid- erations by Casimir, Polder, 9 and Lifshitz. 10 Lifshitz calculated the attractive forces between nonmetallic solids at distances of separation sufficiently large that the phase lag due to the finite velocity of electromagnetic waves becomes a factor. He obtained the following relationship between the attractive force and the known physical constants: where F is the attractive force per unit of area, h is Planck’s constant, C is the velocity of light, d is the distance of separation, e o is the dielectric constant, and φ ( e o ) is a multiplying factor that depends on the dielectric constant as follows: Strictly speaking, the dielectric constant in this expression should be measured at electron orbital frequency, about 10 15 Hz. However, if we assume handbook values of the dielectric constant at 10 6 Hz, which for nylon, polyethylene, and polytetrafluoroethylene, are 3.5, 2.3, and 2.0, respectively, the corre- sponding φ ( e o ) values are 0.37, 0.36, and 0.35. The force values then stand in the ratios 0.11 to 0.056 to 0.039. When normalized to F (nylon) = 1.0, they fall to the following ratios: F (nylon), = 1.00; F (PE), 0.51; F (PTFE), 0.35 When the γ c values (dynes/cm) of these three materials are similarly normalized to the γ c values for nylon, the values fall in remarkedly similar ratios. 1/ e o :00.025 0.10 0.25 0.50 1 φ ( e o ): 1 0.53 0.41 0.37 0.35 0.35 Nylon PE PTFE γ c γ c (norm) 56 1.00 31 0.55 18.5 0.33 U r nt P = −2 12 3 µµ U kTr K == − Keesom potential 2 3 1 2 1 2 6 µµ U r 1 1 2 22 2 1 6 = −+µα µα F hc e e de oo o = − + πφ 2 4 1 240 1 ()[()] () DK4036_book.fm Page 4 Monday, April 25, 2005 12:18 PM © 2006 by Taylor & Francis Group, LLC The Theory of Adhesion 5 -5 In the Lifshitz equation, the force of attraction is shown to decrease as the inverse fourth power of the distance of separation. However, when the separation becomes so small that the phase lag in the inter- action no longer is significant (it is of the order of 6 ° at a separation of 50 Å), the attractive force varies as the inverse third power of the distance of separation. This has been verified experimentally, 11 although the direct measurement is extremely difficult (Figure 5.4). The forces existing at separations greater than 50 Å contribute very little to adhesion. Some 30 years ago Good and Girifalco reexamined the interfacial tensions between dissimilar liquids and developed a theory of adhesion. 12 They found that the work of adhesion, given by could be approximated quite well by the geometric mean of the works of cohesion of the two liquids when the only attractive forces of cohesion are dispersion forces: However, in some liquid pairs (e.g., water and hydrocarbons), this did not hold, and they coined an “interaction parameter,” Φ , given by Thus, FIGURE 5.4 Attraction between ideally planar solids. Separation in Angstrom Units 250 200 100 50 20 110 100 1000 Force Constant D 4.07 1 F∝ D 2.94 1 F∝ W aLL LL =+−γγγ 1212 W aLL = 2 12 12 () / γγ Φ= +−γγγ γγ LL LL LL 1212 12 2 12 () / W aLL = 2 12 12 Φ() / γγ DK4036_book.fm Page 5 Monday, April 25, 2005 12:18 PM © 2006 by Taylor & Francis Group, LLC 5 -6 Coatings Technology Handbook, Third Edition For water on a paraffinic hydrocarbon, where the contact angle is 108 ° , Φ would have a value of about 0.55. For hexadecane on polyethylene, Φ is very near unity. Good and his associates 11,12 have provided directions for calculating Φ , and they give experimental and calculated values for several combinations of water and organic liquids. Fowkes 13 approached the problem from a different point of view. He reasoned that the only forces operable at the interface between water and an aliphatic hydrocarbon molecule contain no hydrogen bonding groups and no fixed dipoles. Fowkes also assumed that the work of adhesion would be given by twice the geometric mean of the surface energies of the two liquids on either side of the interface but now taking into consideration only the dispersion force components of the surface energies. For the work of adhesion between water (L 1 ) and n-octane (L 2 ), we have where the superscript D stands for the dispersion energy component of the total surface energy. Accepted values for the surface energies and interfacial energies are as follows: If these values are substituted into the equation above to solve for we get 22.0 ergs/cm 2 . Fowkes evaluated several water-aliphatic hydrocarbon systems and found that they all yielded essentially the same value for the dispersion energy component of the surface energy of water, 21.8 ± 0.7 ergs/cm 2 . Tur ning now to the work of adhesion and the interfacial energy between mercury and aliphatic hydrocarbon, Fowkes calculated the dispersion energy component of the surface energy of mercury. Using n-octane as the hydrocarbon liquid having a surface energy of 21.8 ergs/cm 2 (all of it attributed to dispersion forces), the surface energy of mercury, 484 ergs/cm 2 , and the interfacial energy, 375 ergs/cm 2 , we have The average for a series of mercury–aliphatic hydrocarbon systems yielded 200 ± 7 ergs/cm 2 for the dispersion energy component of the surface energy of mercury. Since the remaining forces that contribute to the surface energy of mercury are metallic forces, the only interacting forces at the water–mercury interface are the dispersion forces, and the work of adhesion is given by from which This compares very favorably with the measured value of 426 ergs/cm 2 . W aL D L D LLL ==−2 12 1 12 12 () / γγ γ γ γγγγ LLL D L 122 72 8 21 8 2 ===.; .;ergs/cm ergs/cm 2 112 50 8 L = .ergs/cm 2 γ HO 2 D , W a D n D Hg n Hg n ==+− −−− 2 12 () / (, γγ γ γ γ Hg oct oct oct) WW a D D =× =+− = 2218484 21 8 375 196 2 12 (.) . . / γ γ Hg Hg γ Hg D W aHHO g =× =+−2 200 21 8 484 72 8 12 2 (.) . / (, ) γ γ (, ) . HHO g 2 424 7= ergs/cm 2 DK4036_book.fm Page 6 Monday, April 25, 2005 12:18 PM © 2006 by Taylor & Francis Group, LLC The Theory of Adhesion 5-7 The work of adhesion due to dispersion forces is numerically small in work or energy units. For example, the work of adhesion of methylene iodide on polyethylene is 82 ergs/cm 2 (θ = 52°). This small value is not, however, indicative of a small force of attraction across the interface. Keep in mind that the work is the product of force and displacement, and that the attractive force, at separation distances less than 50 Å (5 × 10 −7 cm) increases as the inverse of displacement raised to the third The molecules at the interface are at an equilibrium distance of separation where attractive forces and repulsive forces balance. The variation in the repulsive forces with distance of separation has a dependence several orders of magnitude higher than the attractive forces (of the order of 10 12 for atom pairs and 10 8 for repulsion forces across a hypothetical plane). We can calculate the maximum force of attraction by equating the work of adhesion to the work of separation. Let F a indicate the attractive force, F r the repulsive force, x the distance separation, and d the equilibrium distance. We cannot measure d directly, but we can estimate it from calculations of the distance between molecular centers in a liquid of known specific gravity and molecular weight. In the case of methylene iodide (sp g 3.325, mol 267.9), we calculate the separation to be about 5 × 10 −8 cm between the centers of adjacent molecules. If we take 5 × 10 −8 cm as a reasonable distance of separation across the interface between methylene iodide and polyethylene, and we accept the force versus distance relationships for attraction (a) and repulsion (r), we can write: where the subscript e stands for “equilibrium.” At equilibrium we have the condition that (F a ) e = (F r ) e . We can then express the work of adhesion as The solution is For methylene iodide on polyethylene, W a is 82 ergs/cm 2 . Taking d as 5 × 10 −8 cm, F e = F = F r = 4.92 × 10 9 dynes/cm 2 . The maximum attractive force is encountered where the difference between the attractive forces and the repulsive forces maximizes as separation proceeds. This occurs where (d/x) 3 − (d/x) 8 maximizes, at about x = 1.22d. At this displacement, F = 0.347F e , or, in the case of methylene iodide and polyethylene, at 1.71 × 10 9 dynes/cm 2 (about 25,000 psi). This would be the maximum attractive force experienced when separation of the materials is attempted; it far exceeds the average stresses that are typically observed when adhesive bonds are broken. Others have calculated theoretical forces of adhesion by other approaches. All yield results that predict breaking strength far exceeding the measured breaking strengths. FF d x FF d x aae rre =       =       () () 3 8 WF d x dx F d x dx ae e dd =       −       ∞∞ ∫∫ () () 38 WF dd ae =−       27 DK4036_book.fm Page 7 Monday, April 25, 2005 12:18 PM © 2006 by Taylor & Francis Group, LLC power (Figure 5.4). 6 -1 6 Adhesion Testing 6.1 Fundamentals of Adhesion 6- 1 6.2 Standardization of Adhesion Tests 6- 3 6.3 Delamination Procedures 6- 4 6.4 Local Debonding Systems 6- 7 6.5 Flaw Detection Methods 6- 10 6.6 Outlook 6- 12 References 6- 13 6.1 Fundamentals of Adhesion Without sufficient adhesion, a coating of otherwise excellent properties in terms of resistance to weather, chemicals, scratches, or impact would be rather worthless. It is therefore necessary to provide for good adhesion features when paint materials are formulated. There must also be adequate means for controlling the level of adhesion strength after the coating has been spread and cured on the substrate. Moreover, methods should be available that allow for the detection of any failure in the case of the dissolution of the bond between coating and substrate, under any circumstances whatsoever. 6.1.1 Components at the Interface In chemical terms, there is a considerable similarity between paints on one side and adhesives or glues in this chapter to concentrate on the behavior of paint materials. Adhesion is the property requested in either case, though perhaps with different emphasis on its intensity, according to the intended use. Such a coating is, in essence, a polymer consisting of more or less cross-linked macromolecules and a certain amount of pigments and fillers. Metals, woods, plastics, paper, leather, concrete, or masonry, to name only the most important materials, can form the substrate for the coating. It is important, however, to keep in mind that these substrate materials may inhibit a rigidity higher than that of the coating. Under such conditions, fracture will occur within the coating, if the system experiences external force of sufficient intensity. Cohesive failure will be the consequence, however, if the adhesion at the interface surpasses the cohesion of the paint layer. Otherwise, adhesive failure is obtained, indicating a definite separation between coating and substrate. Ulrich Zorll Forschungsinstitut für Pigmente and Lacke DK4036_book.fm Page 1 Monday, April 25, 2005 12:18 PM © 2006 by Taylor & Francis Group, LLC Components at the Interface • Causes of Failure • Measures of Cross-Cut Test • Tensile Methods Adhesion Scratch Technique • Indentation Debonding • Impact Tests Ultrasonic Pulse-Echo System • Acoustic Emission Analysis • Knife-Cutting Method • Peel Test • Blister Method Thermographic Detection of Defects on the other (Figure 6.1). Both materials appear in the form of organic coatings; thus, it is appropriate 7 -1 7 Coating Calculations 7.1 Introduction 7- 1 7.2 Resins 7- 1 7.3 Pigments 7- 2 7.4 Solvents 7- 2 7.5 Additives 7- 2 7.6 7.7 Calculations 7- 2 7.8 Converting to a 100 Gallon Formulation 7- 4 7.9 Cost 7- 4 7.10 Coverage 7- 5 7.11 Computer Use 7- 5 Bibliography 7- 5 7.1 Introduction Coatings are defined as mixtures of various materials. The questions arise as to how much of which materials, and how do these things relate. The materials fall into four general categories, as follows: •Resins • Pigments •Solvents •Additives 7.2 Resins These are the generally solid, sticky materials that hold the system together. They are also called binders, and when in a solvent, they are the vehicles for the system. They may come as a “single-package” or “two- package” system. Single package is just the liquid resin or the resin in solvent. Two package means that an “A” part was blended with a “B” part to cause a chemical reaction. In both systems, we need to know the amount of solid resin present. This dry material divided by the total of the dry plus the solvent is frequently called a “resin solid.” With the two-package systems, we need to know not only the solids but also the ratio of these solids to form the desired film. This ratio may be designated as a simple ratio of 1 to 1. Or it may be based on 1 or 100, as 0.3 to 1, or 30 parts per hundred, or a total of 100 as 43 to 57. These ratios determine the film properties. We will also need to know the density (weight per unit volume, usually as pounds per gallon) of the resin or vehicle to help calculate volume. Arthur A. Tracton Consultant DK4036_book.fm Page 1 Monday, April 25, 2005 12:18 PM © 2006 by Taylor & Francis Group, LLC Formulation Weight • Formulation Volume • Formulation Density • Formulation of “Nonvolatile by Weight” • Ratio (Weight) • Pigment Volume Content (Volume) Conventions 7-2 Formulation “Nonvolatile by Volume” • Pigment to Binder Coating Calculations 7 -3 TA B LE 7.1 Paint Formulation Calculations No. Constants Calculations Material lb/gal gal/lb %NV Cost, $/lb Weight Volume Dry Weight Dry Volume #/100 gal gal/100 gal Cost/gal 1Titanium Dioxide 34.99 0.029 100 $1.15 100 2.86 100 2.86 196.00 5.6 2.25 2 Phthalocyanine Blue 12.99 0.077 100 $10.55 50 3.85 50 3.85 98.00 7.5 10.34 3Acrylic Resin Solution 9.05 0.11 50 $1.09 300 33.15 150 16.58 588.00 65.0 6.41 4Toluene 7.55 0.132 0 $0.28 20 2.65 0 0.0 39.20 5.2 0.11 5Butoxyethanol 7.51 0.133 0 $0.75 30 3.99 0 0 .0 58.80 7.8 0.44 6Methyl Ethyl Ketone 6.71 0.149 0 $0.55 30 4.47 0 0 .0 58.80 8.8 0.32 7 8 9 10 Total X X X X 530 50.97 300 23.29 1038.8 99.9 19.88 Factor = 1.96 On Total Formulation a% Nonvolatile Weight 56.60 b% Nonvolatile Volume 45.69 c Pigment/Binder Ratio 2 to 3 d Pigment Volume Content 28.81 eDensity, lb/gal 10.4 fsquare feet/gal @ 1 mil dry 733 DK4036_book.fm Page 3 Monday, April 25, 2005 12:18 PM © 2006 by Taylor & Francis Group, LLC [...]... 69.5 528 4 525 0 0 34.3 127 3699 0.5865 623 28 0.87868 427 8 0 0 0 Coatings Technology Handbook, Third Edition Total Calculations % % Cost, Solvent Water $/lb DK4036_book.fm Page 6 Monday, April 25 , 20 05 12: 18 PM 7-6 TABLE 7 .2 DK4036_book.fm Page 1 Monday, April 25 , 20 05 12: 18 PM 8 Infrared Spectroscopy of Coatings 8.1 8 .2 8.3 Introduction 8-1 Principles 8-1 Instrumentation 8 -2 8.4... Water 8.896797153 1.148105 626 9.047619048 0.0076 923 08 0 0.007094784 0. 022 294118 0 0 0 347.76 115. 92 440.50 0.46 34.31 1.17 1.76 0.00 0.00 0.00 41 .25 13.31 41.95 0.04 3.18 0.07 0 .21 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 0 0 0 0 0 0 0 0 0 0 180. 42 19. 129 60304 941.89 100.00 $0.00 0 105.330 828 9 factor = 4.63685635 cost/gal $0.00 88.817 88.701 0.51 95 90 0 .22 2. 87 10.05 VOC = 1.05 lbs/gal... 50 25 50 75 1.00 2 Concentration g/m FIGURE 11 .2 Differences in sensitivities in products from different suppliers of silicone 20 0 X-Ray CPS 150 100 50 25 50 Concentration g/m2 FIGURE 11.3 Differences in paper backings © 20 06 by Taylor & Francis Group, LLC 75 1.00 DK4036_book.fm Page 1 Monday, April 25 , 20 05 12: 18 PM 12 Sunlight, Ultraviolet, and Accelerated Weathering 12. 1 Introduction 12- 1... 12. 1 Introduction 12- 1 12. 2 Sunlight 12- 1 Variability of Sunlight 12. 3 Accelerated Light Sources Compared to Sunlight 12- 2 The Importance of Short-Wavelength Cutoff 12. 4 Arc-Type Light Sources 12- 4 Enclosed Carbon Arc (ASTM G 153) • Sunshine Carbon Arc (Open Flame Carbon Arc: ASTM G 1 52) • Xenon Arc (ASTM G 155) 12. 5 Fluorescent UV Lamps . 12- 7 Patrick Brennan Q-Panel Lab... For silicone coatings and titanium dioxide in paper, an iron-55 (Fe-55) source is used Fe-55 x-rays are soft (low energy) and do not penetrate far into a sample For silver on film, a more energetic americanum241 source has been used 11-1 © 20 06 by Taylor & Francis Group, LLC DK4036_book.fm Page 4 Monday, April 25 , 20 05 12: 18 PM 11-4 Coatings Technology Handbook, Third Edition Vendor A 20 0 Vendor B 150...Paint Formulation Constants No 1 2 3 4 5 6 7 8 9 10 Material lb/gal gal/lb Gloss Varnish 8.43 0.118 623 9 62 Resin @ 40% in BCarbAc 8.71 0.114810563 Titanium Dioxide 10.5 0.09 523 8095 Antiskin Agent 13 0.076 923 077 Butyl Carbitol Acetate 10.8 0.0 925 925 93 Cobalt Drier, 6% 17.83 0.05608 525 Lead Drier, 12% 8.5 0.117647059 X Total Formulation lb/gal 9. 42 % Nonvolatile weight % Nonvolatile volume... vol binder vol pigment + binder % Water 0.00 % Solvent 11.18 © 20 06 by Taylor & Francis Group, LLC X %NV 1 0.4 1 1 0 0.5 0.5 X 0 0.6 0 0 1 0.5 0.5 0 0 0 0 0 0 0 X $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 X Weight 75 25 95 0.1 7.4 0 .25 3 0.379 Gallons 8.896797153 2. 87 026 4064 9.047619048 0.0076 923 08 0.685185185 0.014189568 0.04458 823 5 20 3.1 32 21.56633556 Dry Wt 75.00 10.00 95.00 0.10 0.00 0.13 0.19 0.00... procedure 9-1 © 20 06 by Taylor & Francis Group, LLC DK4036_book.fm Page 4 Monday, April 25 , 20 05 12: 18 PM 9-4 Coatings Technology Handbook, Third Edition Colborn, Robert, Modern Science and Technology Princeton, NJ: Van Nostrand, 1965 Foreman, Jon, “Dynamic mechanical analysis of polymers,” American Laboratory, January 1997, p 21 Hassel, Robert L., “Evaluation of polymer flammability by thermal analysis,” American... Soc Forensic Sci., 27 , 20 9 (1994) 48 J A Payne, L F Francis, and A V McCormick, J Appl Polym Sci., 66, 126 7 (1997) 49 G A George, G A Cash, and L Rintoul, Polym Int., 41, 1 62 (1996) 50 J L Gerlock, C A Smith, E M Nunez, V A Cooper, P Liscombe, D R Cummings, and T G Dusibiber, Adv Chem Ser., 24 9, 335 (1996) 51 A A Dias, H Hartwig, and J F G A Jansen, Surf Coat Int., 83, 3 82 (20 00) 52 R J Dick, K J Heater,... TGA; TA- 121 , Oxidation Stability of Polyethylene Terephthalate; TA- 123 , Determination of Polymer Crystallinity by DSC; TA- 125 , Estimation of Polymer Lifetime by TGA Decomposition Kinetics; TA-134, Kinetics of Drying by TGA; and TA-135, Use of TGA to Distinguish Flame-Retardant Polymers from Standard Polymers © 20 06 by Taylor & Francis Group, LLC DK4036_book.fm Page 1 Monday, April 25 , 20 05 12: 18 PM . Angstrom Units 25 0 20 0 100 50 20 110 100 1000 Force Constant D 4.07 1 F∝ D 2. 94 1 F∝ W aLL LL =+−γγγ 121 2 W aLL = 2 12 12 () / γγ Φ= +−γγγ γγ LL LL LL 121 2 12 2 12 () / W aLL = 2 12 12 Φ() / γγ . value of 426 ergs/cm 2 . W aL D L D LLL == 2 12 1 12 12 () / γγ γ γ γγγγ LLL D L 122 72 8 21 8 2 ===.; .;ergs/cm ergs/cm 2 1 12 50 8 L = .ergs/cm 2 γ HO 2 D , W a D n D Hg n Hg n ==+− −−− 2 12 () / (, γγ. =+− = 22 18484 21 8 375 196 2 12 (.) . . / γ γ Hg Hg γ Hg D W aHHO g =× =+ 2 200 21 8 484 72 8 12 2 (.) . / (, ) γ γ (, ) . HHO g 2 424 7= ergs/cm 2 DK4036_book.fm Page 6 Monday, April 25 , 20 05 12: 18