Ind. Eng. Chem. Res. 2001, 40, 21-25
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Prediction of Environmental Stress Cracking in Plastics with Hansen Solubility Parameters Charles M. Hansen and Lisbeth Just FORCE Institute, Brøndby, Denmark
The results reported here confirm that environmental stress cracking phenomena in plastics depend on the size and shape of the test liquid’s molecules as well as their Hansen solubility parameters (HSP) relative to those of the polymer. The behavior of other, untested liquids can be estimated from HSP correlations based on a limited number of test liquids. A simple test has been developed for the cracking tendency of immersed polymer tubes having different levels of externally applied, controlled stresses. This uses standard tapered NS Teflon (most glass is too rough) stoppers placed on a toploader analytical balance. Polymer tubes are pressed onto the stoppers until the balance shows the given desired force. The tube and stopper are then immersed in a test liquid and observed at regular time intervals for cracking. It has been assumed that the Teflon stoppers are inert in this application. The experiments described here used a COC (cyclo-olefinic copolymer) type polymer (Topas 6013, Ticona). The samples cracked in a number of solvents without external stress. Methyl isobutyl ketone gives rapid cracking of tubes of this polymer at low external stress while olive oil, for example, is somewhat slower to give cracking and requires moderate external stress and longer times. Background There are several reports in the literature which indicate that the Hansen solubility parameters (HSP) as well as the size and shape of the challenging liquid molecules play an important role in environmental stress cracking (ESC).1,2 A more recent study3 discusses both HSP and the various standards useful in the testing of ESC in medical plastics. These include the following: (a) ASTM D 1693 Environmental Stress Cracking of Ethylene Plastics; (b) ISO 4600 Resistance to ESCsBall/Pin Impression Method; (c) ISO 6252 Resistance to ESCsConstant-Tensile-Stress Method; (d) ISO 4599 Resistance to ESCsBent-Strip Method. In addition to these, ref 3 includes an extensive literature review of ESC which will not be repeated here. These standards involve bending tests with the exception of ISO 4600, where a hole is drilled in a plastic sheet. A ball or pin is then forced into the hole, and the piece can then be exposed to given media. The test proposed below, involving forcing a standard taper NS Teflon stopper placed on a toploader analytical balance into the tube to a given load, can be considered an extension of this procedure applied to polymer tubes. Data for ESC are also presented in ref 3 for poly(ethylene terephthalate) (PET), glycol modified poly(cyclohexylenedimethylene terephthalate (PCTG) (a copolyester), and polycarbonate. The conclusions of the work in ref 3 include “the solubility parameter approach is only modestly useful for correlating stress-cracking behavior with the ability of a liquid to swell a plastic” and “for a given medical application, the optimal test method will depend on the failure criteria established by the designers of the component or device”. These conclusions are correct. For improved understanding and predictability, the solubility parameter approach generally must be combined with the size and shape of the liquid molecules, these being important factors in determining how rapidly the absorption will take place. In addition, the use of HSP rather than total solubility
parameters is recommended. The correlations presented, for example, can be used to predict behavior in the more than 800 liquids whose HSP are reported in.4 The polymer selected for this study was a clear cycloolefinic copolymer (COC) type (Topas 6013, Ticona). The physical property data on this polymer are reported in ref 5, although the molecular weight and glass transition temperatures, which are important for this type of behavior, are not included. The heat deflection temperature under load [DTUL/B (0.46 MPa) ISO 75 parts 1 and 2] is reported as 130 °C. Injection-molded tubes of this polymer were used in the testing. The scope of the study did not allow development of a complete understanding of the mechanisms involved in the test method. As discussed later, there appears to be some potential for new information from the test method, for which reason its further study appears warranted. HSP The total cohesion energy of a liquid, E, can be divided into at least three separate parts either by experiment or by calculation.4 In the three-parameter Hansen approach, these parts quantitatively describe the nonpolar (atomic), dispersion interactions, ED, permanent dipole-permanent dipole (molecular) interactions, EP, and the hydrogen-bonding (molecular) interactions, EH.
E ) ED + EP + EH
(1)
Dividing eq 1 by the molar volume, V, gives the respective Hansen cohesion energy (solubility) parameters.
E/V ) ED/V + EP/V + EH/V
(2)
δ2 ) δD2 + δP2 + δH2
(3)
The total cohesion energy divided by the molar volume is the total cohesion energy density. The square root of
10.1021/ie9904955 CCC: $20.00 © 2001 American Chemical Society Published on Web 11/22/2000
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Ind. Eng. Chem. Res., Vol. 40, No. 1, 2001
this is the Hildebrand total solubility parameter, δ. The SI units for all of these are MPa1/2. HSP can be readily calculated for liquids or measured for polymers. These parameters can also be assigned to aromas, low molecular weight solids, gases, or other materials of wide interest. Expected relative solubility (and stress cracking) properties can be conveniently visualized using a spherical characterization for a polymer. Its HSP are at the center of the sphere, and the radius of the sphere, Ro, indicates the maximum difference in affinity tolerable for the solution (stress cracking) to take place. A simple composite affinity parameter, the RED (relative energy difference) number, has been defined as the distance according to eq 4, Ra, divided by Ro. The RED number is given by eq 5. The equation for Ra is
Ra2 ) 4(δD1 - δD2)2 + (δP1 - δP2)2 + (δH1 - δH2)2 (4) and
RED ) Ra/Ro
(5)
The subscripts 1 and 2 are for the polymer and challenge chemical, respectively. For those familiar with the widely used Flory interaction coefficient, χ, it may be noted that there is a relation between this and the RED number given by eq 6. χc is
χ ) χcRED2
(6)
usually taken as being near 1/2 for polymers of very large molecular weight. Unfortunately, χ does not explicitly take into account hydrogen bonding, for example. The above equation is, therefore, only indicative of a relation had the Flory-Huggins approach included polar and hydrogen-bonding interactions explicitly. The coefficient “4” in eq 4 has been found to be correct for all practical purposes in over 1000 correlations using HSP. The coefficient “4” (or 0.25) is predicted theoretically by the Prigogine corresponding states theory of polymer solutions for specific interactions (i.e., those derived from differences in δP and δH in HSP terminology)6-8 and can also be traced back to still earlier approaches (Lorentz-Berthelot mixtures) studying affinities among gases, for example.9 The so-called geometric mean to estimate the interaction between two unlike species is used in all of these, and the coefficient “4” experimentally confirms that this type of mean is also valid for hydrogen-bonding interactions. The coefficient “4” must be used to differentiate the behavior of the atomic (dispersion or London) type forces from that of the molecular dipolar and molecular hydrogenbonding forces. The HSP approach can no longer be considered empirical, with the present report being still another demonstration of its ability to correlate the behavior of all types of liquids with respect to their effects on a given polymer. The Flory approach seems inadequate, because it does not include hydrogen bonding explicitly, and the Prigogine approach is too difficult to use and lacks specific consideration of hydrogen bonding as well. This leaves the HSP approach as the only reliable and generally useful means to study the type of interactions involved in this paper. The above discussion is included in ref 4 in expanded form.
HSP Related to Stress Cracking A study of stress cracking in Nylon 6,6 found the phenomena to be related not only to HSP but also to the rate of uptake of given liquids.1 Reasonably rapid uptake of test liquids could rapidly plasticize the polymer, so that cracking was avoided. We have also noted this behavior in the present study. Larger differences in HSP between the polymer and the test liquid were generally found to require larger stresses (critical strains) to initiate stress cracking. The rate of uptake is dependent both on the surface concentration on contact with the liquid (solubility) and on its molecular size and shape (the diffusion coefficient is lower for larger and more bulky molecular structure). The surface solubility is higher for better matches in solubility parameters between the polymer and the liquid to which it is exposed. These general results have also been confirmed by numerous studies discussed in the general reference book by Barton.2 There is a consensus among several authors, also reconfirmed here, that “There is a small central zone in these.. (HSP).. plots for dissolution, a boundary region of solvent crazing, and an intermediate zone of predominately solvent cracking with some dissolution, swelling, and crazing.” The polymers studied included polysulfone and polycarbonate. Other studies referenced include correlations with ESC and solubility parameters for such varied polymer types as rubber-modified styrene-acrylonitrile, PET, poly(methyl methacrylate), polystyrene, and rigid poly(vinyl chloride). Such correlations with HSP seem to be valid on a very general basis. Results and Discussion The COC polymer dissolved in 8 of the 43 test liquids. These data are presented in Table 1. They have been used to generate a HSP correlation for the solubility of the polymer. Data for this correlation are included as the first entry in Table 2. A data fit of 1.000 is found when all of the “good” solvents are located within the sphere of the correlation and all of the “bad” solvents are found outside of the sphere. This was the case here, although the severe swelling and deformation which was found for tetrahydrofuran as discussed further later was not considered as dissolving in this correlation. In addition to these most aggressive liquids, it was found that cracking occurred very shortly after or in connection with immersion in several of the other test liquids. No external stress was applied. No further changes in behavior were observed after 2 days of immersion time. A second type of correlation was then made by grouping the liquids which caused cracking with those which dissolved the polymer into a single group of aggressive solvents. Tetrahydrofuran did not produce cracking as discussed further later, but it is included here as an aggressive solvent. Table 1 also reports these experimental results, and the corresponding HSP correlation is included in Table 2. This correlation of stress cracking (plus solubility) is the basis of the discussion that follows. The results of these correlations are portrayed in Figure 1, where the shaded solubility region is surrounded by a clear region where ESC can be expected. The initial stress level of these tubes is not known in absolute terms, and a new HSP correlation could be generated for aggressive liquids at a higher stress level.
Ind. Eng. Chem. Res., Vol. 40, No. 1, 2001 23 Table 1. Data Used for HSP Correlations for Solubility and/or Cracking of a COC (Topas 6013, Ticona) Polymer solvent toluene trichloroethylene carbon tetrachloride chlorobenzene chloroform cyclohexane benzene o-dichlorobenzene butyl acetate methyl isobutyl ketone methylene dichloride ethylene dichloride hexane ethyl acetate diethyl ether 1,4-dioxane tetrahydrofuran acetophenone isophorone nitrobenzene 2-nitropropane acetone diacetone alcohol methyl-2-pyrrolidone ethylene glycol monobutyl ether cyclohexanol nitroethane ethylene glycol monoethyl ether dimethylformamide 1-butanol γ-butyrolactone ethylene glycol monomethyl ether dimethyl sulfoxide propylene carbonate nitromethane dipropylene glycol ethanol diethylene glycol propylene glycol methanol ethanolamine ethylene glycol formamide
δD
δP
δH
SOLUB/ CRACKSa RED
Vb
18.0 1.4 2.0 18.0 3.1 5.3 17.8 0.0 0.6 19.0 4.3 2.0 17.8 3.1 5.7 16.8 0.0 0.2 18.4 0.0 2.0 19.2 6.3 3.3 15.8 3.7 6.3 15.3 6.1 4.1 18.2 6.3 6.1 19.0 7.4 4.1 14.9 0.0 0.0 15.8 5.3 7.2 14.5 2.9 5.1 19.0 1.8 7.4 16.8 5.7 8.0 19.6 8.6 3.7 16.6 8.2 7.4 20.0 8.6 4.1 16.2 12.1 4.1 15.5 10.4 7.0 15.8 8.2 10.8 18.0 12.3 7.2 16.0 5.1 12.3
1 1 1 1 1 1 1 1 C 0* C C C C C 0 D* 0 0 0 0 0 0 0 0
0.344 0.546 0.560 0.564 0.584 0.589 0.594 0.799 0.812 0.841 0.848 0.912 0.951 0.986 0.993 1.005 1.019 1.148 1.170 1.244 1.481 1.484 1.644 1.658 1.674
17.4 4.1 13.5 16.0 15.5 4.5 16.2 9.2 14.3
0 0 0
1.788 106 2.015 71 2.159 97
17.4 13.7 11.3 16.0 5.7 15.8 19.0 16.6 7.4 16.2 9.2 16.4
0 0 0 0
2.193 2.216 2.328 2.453
18.4 20.0 15.8 16.5 15.8 16.6 16.8 15.1 17.0 17.0 17.2
0 0 0 0 0 0 0 0 0 0 0
2.457 71 2.496 85 2.541 54 2.716 130 2.884 58 3.229 94 3.459 73 3.536 40 3.559 59 3.934 55 4.472 39
16.4 18.0 18.8 10.6 8.8 12.0 9.4 12.3 15.5 11.0 26.2
10.2 4.1 5.1 17.7 19.4 20.7 23.3 22.3 21.2 26.0 19.0
106 90 97 102 80 108 89 112 132 125 63 79 131 98 104 85 81 117 150 102 86 74 124 96 131
77 91 76 79
Table 2. Comparison of HSP Correlations for Selected Materialsa polymer
δD
δP
δH
Ro
FIT
G/Tb
Topas 6013, solubility Topas 6013, solubility + cracks PP > 0.5% uptake olive oil solubility PET critical strain < 0.60%d PCTG critical strain < 0.55%d PCTG critical strain < 0.50%d PC critical strain < 0.31%d PEI Ultem 1000 600 psie PEI Ultem 1000 1200 psie PEI Ultem 1000 2500 psie PEI Ultem 1000 solubilityf
18.0 17.3
3.0 3.1
2.0 2.1
5.0 6.4
1.000 0.974
8/43 15/43
18.0 15.9 21.3
3.0 1.2 4.5
3.0 5.4 12.3
8.0 12.0 13.9
1.000 1.000 1.000
13/21 c 12/19
18.3
9.3
11.3
8.0
1.000
8/19
18.8
8.8
10.8
7.9
0.989
6/19
18.0
9.0
6.0
10.0
1.000
9/18
17.3
5.3
4.7
3.3
1.000
3/20
17.0
6.0
4.0
4.0
1.000
4/20
17.4
4.6
9.0
7.2
0.967
9/20
19.6
7.6
9.0
6.0
0.952
8/45
a These correlations can be used to predict the behavior of over 800 liquids whose HSP are reported in ref 4. b G/T is the number of “good” or attacking solvents relative to the total number of solvent data points used in the correlation. c Older correlation; these data were not recorded at that time. d Data for this correlation found in ref 3. e Correlations reported in ref 4 based on data from ref 10. Too few data. See discussion in the text. Ultem is a registered trademark of General Electric Co. f Data from complete HSP determination of solubility.
a In the SOLUB/CRACKS column a “1” indicates solubility, a “C” indicates cracking in the given liquid without external stress, a “D” indicates severe deformation and swelling, and a “0” indicates no significant effect. The asterisks indicate data which does not conform strictly to the model; attack only by solvents with RED numbers of less than 1.0. A line in the table at RED ) 1.0 would separate the liquids into two groups, those “predicted as aggressive” and those “predicted as nonaggressive”. HSP correlations allow predictions for any liquid whose HSP is known. b V is the molar volume of the given liquid in cm3/mol.
Ro for the cracking + solution correlation is 6.4, which is somewhat larger than the 5.0 radius found for solubility only. This is expected. The data fit (FIT) of 0.974 is good. As stated previously, this would have been 1.0 for all of the attacking solvents within the sphere and all of the nonattacking solvents outside of it. The solvents classified as “1” in the SOLUB/CRACK column were those which dissolved the polymer. Those solvents indicated with a “C” cracked the polymer. Other liquids can be absorbed but in smaller amounts so that there is no cracking. The molecular volume (V) is also included in Table 1 as an approximate size parameter. An asterisk indicates those liquids which do not comply with the model (outliers) and, therefore, contribute to a lower FIT. The solvent contributing almost all of the error in this correlation is methyl isobutyl ketone (MIBK). This is clearly seen in Table 1, where the
Figure 1. Solubility parameters which correlate both solubility (inner sphere) and ESC and solubility (outer sphere). The liquids which crack the polymer without application of external stress have HSP placing them in the clear shell in the figure.
liquids are arranged in order of increasing RED number. The reason for this is that it has a relatively large molar volume and a shape which prevents rapid diffusion. It has been confirmed that this solvent does crack the parts rapidly at slightly elevated stress levels, which makes it a candidate for a rapid test method to evaluate a stress level higher than that of the tubes as supplied. The RED number gives a rapid indication of the solvent quality. Liquids with RED numbers of less than 1.0 are expected to be aggressive in a given correlation.
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Ind. Eng. Chem. Res., Vol. 40, No. 1, 2001
A line at a RED number equal to 1.000 in Table 1 would divide the liquids into those expected to attack and those not expected to attack. It can be seen that the solvents cracking the polymer dominate the RED number range between about 0.8 and 1.0, with the solvents dissolving the polymer having RED numbers of less than 0.8. An exception is tetrahydrofuran, which absorbs very rapidly, thus presumably preventing cracking, but still gives severe deformation/swelling. A “D” in Table 1 indicates this. These immediate effects were not studied. These data are for 23 °C. It was expected that higher temperatures would enlarge the group of solvents leading to solution or cracking, but studies at 37 °C over the same time scale did not confirm this. Stress relaxation would also be more rapid at the higher temperature. The correlations are the same at both temperatures. It is also expected that higher stress levels in the COC polymer will enlarge the group of solvents, leading to cracking, and will make the cracks appear more rapidly. This has not been studied as such on a large scale and in a systematic manner, although some indications that this is true are given in the following. Calculations using eqs 4 and 5 show that the olive oil is expected to just be able to dissolve the COC polymer used in this study. Its molecular size is too large, however. It would also be expected to spontaneously produce cracks if its molecular size were smaller. For this reason and because it is a common household material, we have brought olive oil into focus as a potential test liquid for cracking of stressed COC-type polymers. The RED number for olive oil with regard to the cracking correlation is 0.74. Additional correlations based on cracking under tensile load for PEI Ultem 1000 are included in Table 2. These emphasize the increase in Ro with increasing load. It is clear that the chemical resistance is dependent on the stress level. Higher stress levels lead to a more severe attack by a larger number of chemicals. The solvents considered as being aggressive are those which led to cracking (or other severe attacks) during the study, which lasted 336 h. Some test liquids led to cracking at earlier times, which could be treated in separate correlations, but this has not been done. The correlations all have high data fits. The last entry in Table 2 is for the true solubility of the same polymer. There are more data points in this correlation, and these have been selected from a HSP point of view. The usefulness of the stress cracking correlations is limited because there are limitations on the range of HSP covered in the selection of the 20 test liquids. This is a typical situation found when trying to correlate data found in the literature and has been discussed at some length in ref 4. The solubility correlation more closely reflects the true (thermodynamic) properties of this polymer. Development of a Test Method for ESC None of the test methods in common use listed above were judged satisfactory for evaluating the stress cracking behavior in tubes. It was found that controlled external (internal) stresses could be placed on the tubes by inserting an NS Teflon (most glass is too rough) stopper in the open end of a plastic tube and then pressing this into the tube. Initial exploratory studies without controlled stress levels indicated that MIBK and ethyl acetate would initiate cracking when the Teflon/tube combination was immersed in them. These
liquids would not initiate cracking prior to the insertion of the Teflon stopper nor after the Teflon stopper had been inserted and then removed prior to immersion in the liquids. It was then decided to try to quantify the test method. This was done by pressing a tube onto a Teflon stopper on a toploader analytical balance to some reading (such as 1, 2, or 4 kg). This procedure worked very well and can readily be adopted in systematic testing at different (relative) stress levels. Teflon is wellknown for its resistance to chemicals and should be a satisfactory selection for this purpose. This should be checked, however, in the event that this test does gain wide acceptance. Olive oil would not crack a Topas 6013 tube at a 1 kg level. Levels of 2 and 4 kg with olive oil as the test liquid led to cracking at 2-4 min. Statistical analysis and further study is required to fully evaluate the technique. It seems clear, however, that this is a simple method to evaluate stress cracking in polymer cylinders in a systematic manner. In response to justified reviewer comments, it can be stated that the scope of the study has not allowed evaluation of the state of stresses in the samples nor the degree of orientation in the injection-molded polymer. Likewise, full information will be obtained only when both the stress and strain on the sample are recorded. Some information of this type is found in ref 5 for the polymer in question here. Despite these shortcomings, the results indicate that MIBK, ethyl acetate, or n-butyl acetate will be potential test liquids for very rapid stress cracking of COC-type polymers. They will crack the polymer at low stress levels. Other liquids, such as olive oil, are potential test liquids for measuring higher stresses. Systematic studies and additional correlations can indicate which liquids will crack the polymer when it has a given internal stress. Development of a Test Method for Determining the Absolute Stress in a Plastic Tube The test method described in the previous section places stress on the open end of the tube due to forces applied in an outward direction. If the counterpart of these conditions is used, the external forces can be applied in the opposite direction. In this case, the plastic tube is forced into the female counterpart of the same stopper (if possible). One can establish curves of stress level versus time to cracking for both types of applied stress. These are presumed to be parallel straight lines. The difference between them will be (close to or perhaps equal to) the initial stress present in the plastic tube. This may be a rediscovery of a well-known technique not known to the authors. If not, it is worthy of further study and possible adoption as a standard test method. The requirement of direct measurement of the initial stress level is that the cracking occurs at the same place in both types of experiments. Conclusion ESC in polymers involves both solubility and absorption rate phenomena as well as the state of stress in the polymer. Solubility relations have been correlated with HSP. Absorption rates can be measured or judged on a relative basis, with smaller and more linear molecules diffusing more rapidly than larger and more bulky ones. HSP correlations for solubility and ESC in Topas 6013 tubes have been presented and discussed in detail.
Ind. Eng. Chem. Res., Vol. 40, No. 1, 2001 25
A simple test method for studying ESC in plastic tubes has been developed. This involves pressing the plastic tube and an NS conical Teflon part together with a force measured with a toploader analytical balance. Several liquids of varying severity of attack have been suggested for use in the testing of COC-type polymers based on this test method and the HSP correlations. These include MIBK, ethyl acetate, and n-butyl acetate as the most aggressive and olive oil as moderately aggressive. The more aggressive liquids caused cracking at lower external stress levels. A test method with the potential to establish the level of the initial stresses in a plastic tube has also been suggested. This involves comparison of systematic stress cracking results found from pressing plastic tubes into a female NS conical joint with similar results found from pressing plastic tubes over a male NS conical joint. Full evaluation of this proposed method has not been possible within the scope of this work. Acknowledgment The first version of this paper appeared as an extended abstract for a conference.11 The copyright to ref 11 has been graciously released, and extensions and revisions have been made after constructive reviewer comments. Literature Cited (1) Wyzgoski, M. G. In The Role of Solubility in Stress Cracking of Nylon 6,6. In Macromolecular Solutions; Seymour, R. B., Stahl, G. A., Eds.; Pergamon Press: New York, 1982; pp 41-60.
(2) Barton, A. F. M. Handbook of Solubility Parameters and Other Cohesion Parameters; CRC Press: Boca Raton, FL, 1983; pp 403-408. (3) Moskala, E. J.; Jones, M. Evaluating Environmental Stress Cracking of Medical Plastics. Med. Plast. Biomater. 1998, May, 34-45. (4) Hansen, C. M. Hansen Solubility ParameterssA User’s Handbook; CRC Press: Boca Raton, FL, 1999. (5) Anonymous. Thermoplastic Olefin Polymer of Amorphous Structure Topas (COC); Ticona GmbH: Frankfort am Main, 1997; Sept. (6) Hansen, C. M. PolymeropløselighedsPrigogines Teori om Korresponderende Tilstande og Hansen Opløselighedsparameterteori Bekræfter Hinanden (Polymer SolubilitysPrigogine’s Corresponding States Theory and Hansen Solubility Parameter Theory Confirm Each Other). Dansk Kemi. 1997, 78 (9), 4-6. (7) Prigogine, I. The Molecular Theory of Solutions; Bellemans, A., Mathot, A., Collaborators; North-Holland: Amsterdam, The Netherlands, 1957; Chapter 16, p 17. (8) Patterson, D. Role of Free Volume Changes in Polymer Solution Thermodynamics. J. Polym. Sci., Part C 1968, No. 16, 3379-3389. (9) Rowlinson, J. S. Liquids and Liquid Mixtures; Butterworth Scientific Publications: London, 1959; pp 254-257 and 313-318. (10) Anonymous. Ultem Resin Design Guide; GE Plastics: Pittsfield, MA, 1989. (11) Hansen, C. M.; Just, L. Environmental Stress Cracking in Plastics. Pharmaceutical and Medical Packaging 1999 (Conference Proceedings) Hexagon Holding: Copenhagen, ISBN 87-8975326-7; 1999; Vol. 9, pp 7.1-7.7.
Received for review July 12, 1999 Revised manuscript received March 7, 2000 Accepted May 23, 2000 IE9904955
