Search

The fracture initiation in engineering thermoplastics resulting from chemical degradation is usually observed in the form of a microcrack network within a surface layer of degraded polymer exposed to a combined action of mechanical stresses and chemically aggressive environment. Degradation of polymers is usually manifested in a reduction of molecular weight, increase of crystallinity in semi crystalline polymers, increase of material density, a subtle increase in yield strength, and a dramatic reduction in toughness. An increase in material density, i.e., shrinkage of the degraded layer is constrained by adjacent unchanged material results in a buildup of tensile stress within the degraded layer and compressive stress in the adjacent unchanged material due to increasing incompatibility between the two. These stresses are an addition to preexisting manufacturing and service stresses. At a certain level of degradation, a combination of toughness reduction and increase of tensile stress result in fracture initiation. A quantitative model of the described above processes is presented in these work. For specificity, the internally pressurized plastic pipes that transport a fluid containing a chemically aggressive (oxidizing) agent is used as the model of fracture initiation. Experimental observations of material density and toughness dependence on degradation reported elsewhere are employed in the model. An equation for determination of a critical level of degradation corresponding to the offset of fracture is constructed. The critical level of degradation for fracture initiation depends on the rates of toughness deterioration and build-up of the degradation related stresses as well as on the manufacturing and service stresses. A method for evaluation of the time interval prior to fracture initiation is also formulated.

Small-angle X-ray scattering (SAXS) has been applied in obtaining the solution parameters (molecular mass M, radius of gyration Rg, radius of gyration of cross-section Rq, mass per unit length Mu, and persistence length a ∗ ) of a poly(acrylic acid) (PAA) sample in dioxane at 25°C. The M and Rg values measured from SAXS were 552 000 Da (daltons) and 292 A, respectively. These values are in reasonable agreement with those obtained from solution viscometry measurements on the same sample of PAA in dioxane at 30°C ( M = 567 000 Da and R g = 227 A ). The Rq and a ∗ values obtained from SAXS were 6.1 A and 14.4 A, respectively. The Mu value measured from SAXS is 27.9 Da A−1, in excellent agreement with the model (theoretical) value of 28.6 Da A−1 calculated from the structure and molecular mass of the monomer unit. The length L (= M/Mu = 19 790 A) obtained from SAXS thus corresponds to the contour length of the molecule and not to the ‘hydrodynamic’ length (i.e. the length the chain assumes in the fluid medium).

Several procedures have been previously reported whereby non-isothermal TG (NITG) data can be analyzed for values of the activation energy ( E ) independent of values of the reaction order ( n ). In this paper, other expressions will be derived for the estimation of E which are essentially independent of n -values and are valid at relatively low degrees of conversion. These equations are applied to NITG data for a siloxane and teflon, as well as for theoretical data. The resulting computer and graphical procedures are both utilized to estimate E -values. Limitations of the methods are also mentioned.

Determination des expressions possibles des evaluations simultanee de E et n, qui gardent intacte la fonction d'Arrhenius, mais qui utilisent une expression derivee numerique approximative de l'estimation des courbes de thermogravimetrie

By applying the restriction that α (conversion) = constant to non-isothermal TG (NITG), isothermal TG (ITG) and a combination of both (NITG/ITG), various corresponding expressions have been derived for the evaluation of the activation energy, E . By means of a computer, all the expressions developed were tested against data which was generated from theoretical equations. Also, changes were made in the number of significant figures (s.f.) of data in order to ascertain their effects on values of E . Data were generated and tested for the three theoretical mechanisms, A 2 , F 1 and R 2 .

Determination informatique de la valeur de l'ordre (n) d'une reaction de decomposition unimoleculaire

The kinetics of the acid degradation of Streptococcus salivarius levan was studied by observing changes in the number-average molecular weight, Mn, using end-group analysis. Rate constants for the hydrolysis are presented and a tentative mechanism is forwarded. The data has been analysed according to a statistical model for a polymer with trifunctional branching and it is shown that the hydrolysis of levan proceeds through a mechanism quite different to that reported for the polysaccharide dextran.

A fraction of low molecular weight from a partially acid-hydrolyzed S. salivarius levan was examined in aqueous solution at 25° by the method of small-angle X-ray scattering (SAXS). The weight-average molecular weight of 26,570 and radius of gyration of 47.6 A are in good agreement with the values obtained previously from sedimentation equilibrium and light scattering, respectively. Although this fraction behaves hydrodynamically as a linear random coil, the higher mass per unit length [(mu)b] of 45.82 daltons/A (obtained from SAXS), compared with the calculated value of (mu)l = 28.94 for linear levan, confirms its branched structure. The g-factor, a measure of branching, was computed as 0.63 from the derived expression, g = (mu)l/(mu)b = L/Ll, where L and Ll are the hydrodynamic length (stretched length) of the backbone of the branched levan and linear levan, respectively. The values for persistence length (a* = 17.7 A), radius of gyration of the cross-section (Rq = 8.2 A), and L = 534 A were also obtained for the levan hydrolysate. The lower values of (mu)b = 35.1 A and Rq = 2.3 A, and the higher value of g = 0.90 for the L. mesenteroides dextran hydrolysate of comparable molecular weight, show that the levan hydrolysate is more branched. The higher value of a* = 26.2 A for the dextran suggests that its molecules are stiffer than those of the levan.

Bovine heparin was fractionated according to molecular weight by fractional precipitation utilizing a method described previously. The solution data from sedimentation analysis, intrinsic viscosities and partial specific volumes at pH 2·5 and in 0·5 M NaCl were treated according to the Mandelkern and Flory theory for random coil in calculating the constant β. It was found that the calculated β values for all the fractions were in close agreement with the theoretical value. Based on this observation, the solution data were then treated in light of various hydrodynamic theories for linear polymers to calculate various dimensional and other physical parameters, e.g., ( r 2 ) 1 2 , α (expansion factor), A 2 . In comparing ( r 2 ) 1 2 of a fraction to that calculated from the experimental value of ( s 2 ) 1 2 obtained from low angle X-ray scattering for a comparable molecular weight sample, it was found that heparin in solution with suppressed charges may best be described as approximating the closely related models of Debye and Bueche, Flory and Fox, or Kuhn and Kuhn.

Comparaison avec les methodes graphiques. Utilisation pour la determination des mecanismes de reactions

A novel procedure is presented for the evaluation of kinetic parameters, activation energy ( E ) and reaction order ( n ), from thermogravimetric (TG) traces. From given values of conversion (α) and corresponding temperatures ( T ) are calculated values of E corresponding to various arbitrary values of n . Then, the resulting arbitrary E -values may be plotted against respective n -values and the region bounded by intersecting curves used to simultaneously estimate E and n . This procedure was tested against theoretical data, teflon, sodium bicarbonate, and magnesium hydroxide, and was found to be satisfactory. Some advantages of this method are: it is relatively simple to use; it allows the user to readily discern whether the data are homogeneous and, if not, at what conversions the data deviate. A less sensitive ancillary procedure is also described which can dispense with plotting in the estimation of E and n .

Isotactic poly(1-pentene) was degraded in the presence of pure oxygen at 115°C. The functional groups present in the non-volatile products were identified using infra-red spectroscopy. The volatile products formed were identified by means of a relatively new technique which combines thermal and mass chromatography. In this study, fourteen volatile products were detected and identified and their relative abundance estimated. The results obtained could readily be reproduced. Various oxidation mechanisms for these products are postulated.

The use of linear correlation coefficients to ascertain mechanism from TG data was shown to be unsatisfactory. This is in agreement with results reported by others who also indicated the necessity of using additional isothermal techniques for determining mechanism. Two methods, Reich—Stivala (R—S) and double-log (D-L), were employed to distinguish one mechanism from among 15 theoretical possibilities for heterogeneous solid-state reactions using theoretical TG data. With a certain degree of accuracy of TG data and for relatively large E/RT values (above 18), the R—S method was shown to be superior to the D-L method and a good indicator of a most probable mechanism. In this respect, the utilization of supplemental isothermal techniques may not be necessary when the R—S method is used under certain conditions.

Solution characterization of heparin with high affinity (HA) and low affinity (LA) for antithrombin III was performed using the methods of small-angle x-ray scattering (SAXS), viscometry, and aqueous gel permeation chromatography (GPC). SAXS provided various topological parameters including the radius of gyration ([S2]1/2), radius of gyration of cross-section ([S2]q1/2), persistence length (a*), contour length (L), and mass parameters, e.g., overall molecular mass (Mr), and mass per unit length (Mq). The molecular weights of HA and LA pig mucosal heparins were found to be 14,900 and 11,500 and the respective radii of gyration were 40.1 and 33.6 A. The persistence lengths of HA and LA were 21.3 and 20.3 A, respectively. These parameters were compared to SAXS data of heparin [S. S. Stivala, M. Herbst, O. Kratky, and I. Pilz (1968) Arch. Biochem. Biophys. 127, 795-802] fractionated according to molecular weight only. It was found that the various experimental values of this heparin lie somewhere in between those of HA and LA heparins. It appears that there are no appreciable differences in the physico-chemical properties, including conformation, among the heparins in H2O at 25 degrees C.

The viscosity of heparin was examined in pure glycerol, formamide and in mixtures of the two solvents. This study confirms that the equation η sp c = [η] ∞ [1 + k (c) 1 2 ] , where [η]∞ is the shielded intrinsic viscosity, adequately describes the concentration dependence of the reduced viscosity of the polyelectrolyte, heparin. The [η]∞ linearly increases with the dielectric constant of the solvent.

The kinetics of the thermal oxidation of isotactic poly(1-pentene) was studied in the bulk phase. The experimental data were obtained from the quantitative estimation of carbonyl groups formed in the non-volatile oxidation products using infra-red spectroscopy. Reaction temperature varied from 100° to 115° and oxygen concentrations from 10% to 100% by volume. A general kinetic scheme and mathematical expressions previously reported for the thermal autoxidation of polyolefins satisfactorily explained the experimental results. Activation energies of this polymer for various steps in the kinetic scheme were compared with polypropylene and poly(1-butene).

Small-angle X-ray scattering, SAXS, measurements were obtained from 12-arm near-monodisperse star polystyrenes in methyl ethyl ketone at 25°C. Calculations from the SAXS data yielded information on the molecular weight, Ms, the radius of gyration, Rg, mass per unit length, mu, radius of gyration of the crosssection, Rq, and persistence length, a∗. Values of Ms and Rg from SAXS were in good agreement with values obtained from light scattering. A branching parameter in terms of a∗, s = a∗1a*b where subscripts l and b refer to linear and branch, respectively, is introduced and related in terms of functionability, f, or g, where g = (Rg)b(Rg)l.

The kinetics of the thermal oxidation of isotactic and atactic poly(4-methyl-1-pentene) were studied in the bulk phase using infra-red (i.r.) spectroscopy. The rates of formation of the non-volatile products were assessed from the i.r. bands of the carbonyl groups at different temperatures and various oxygen concentrations. Reaction temperature varied from 120° to 185°C and oxygen concentrations from 10 to 100%, by volume. A general kinetic scheme and mathematical expressions, previously reported for the thermal oxidation of polyolefins, satisfactorily explained the experimental results. Single activation energies for the major oxidation stages in the scheme, were estimated from various Arrhenius plots.

The thermal degradation of the polysaccharide Levan, of various molecular weights, was studied by means of isothermal and dynamic TG, X-ray diffraction, and IR measurements. From dynamic TG traces, two main degradation stages were observed for HL-Levans (hydrolyzed) whereas, three such stages were observed for UL-Levans (unhydrolyzed). These stages were correlated with branching effects, an interpenetrating network, and ring-fragmentation and other reactions in the late stages of the thermal degradation which result in the formation of infusible material that chars on further heating. Isothermal curves obtained for the first stage indicated the possibility of a random type of thermal degradation. Anticipated linear plots were obtained, using expressions from random degradation theory, which added further support for this type of degradation for Levan (stage 1). Various parameters were obtained for the thermal degradation of Levan, e.g., activation energies, and various experimental observations have been correlated in terms of postulated microstructures for Levan and in terms of parameters such as entropy of activation.

A fractionated sample of S. salivarius levan was examined in aqueous solution at 25° by the method of small-angle X-ray scattering. The high molecular weight of 16.9 × 10 6 and low radius of gyration of 395 A suggest that this levan is branched. The mass per unit length [( m u ) b ] was found to be 72.94 daltons/A. Based on the molecular weight of the monomer unit (2,6-anhydro-β- d -fructofuranose) and its length, the mass per unit length of a linear levan [( m u ) l ] was calculated as 28.94 daltons/A. The observation that ( m u ) b > ( m u ) l is a positive indication of branching. The g -factor, a measure of branching, was computed as 0.39 from the derived expression, g = ( m u ) l /( m u ) b = L/L l , where L and L l are the hydrodynamic length (total stretched length) of the backbone of the branched levan and linear levan, respectively. Values of 42.79 A for persistence length, L = 2.313 × 10 5 A, and 22 A for the radius of gyration of the cross-section were also obtained for the branched levan.

Various workers have reported contradictory results for the thermal decomposition of cadmium carbonate (CDC) by means of TG (and DTA). Thus, various activation energies E and mechanisms have been reported for this decomposition. The aim of this paper is to examine various factors which may influence the decomposition of CDC in an attempt to explain the conflicting results previously reported for this decomposition. In this respect, a study of this reaction was made using non-isothermal TG in order to ascertain whether the various factors studied had an appreciable influence on E and mechanism. The various factors employed and discussed were: sample weight, heating rate, type of purge gas, purge gas flow rate and particle size.

The utilization of thermogravimetry should allow an estimate of the extent of reaction for consecutive equations such as based on the amount of gas liberated. An expression was developed for the concurrent determination of the rate constants, k 1 and k 2 , for the above two consecutive irreversible first-order reactions, which required the measurement of reaction rates (slopes). Then a computer algorithm was presented to implement this expression. This algorithm involved a modification of an algorithm previously reported by the authors, and was tested for the cases of theoretical and experimental data. Values of k 1 and k 2 obtained for these cases are compared with assumed and previously reported values.

Comb-branched polystyrenes having both fixed backbone length and number of branches but variable branch lengths were prepared anionically. Small angle X-ray scattering of the model polystyrenes from methyl ethyl ketone (MEK) solutions at 25°C was examined and it is shown that the mass per unit length and cross-sectional radius of gyration increase with increasing branch length. A maximum appears in the Kratky plot for the branched polymers. While the linear polymer displays an essentially Gaussian segment distribution in solution, the branched polymers deviate considerably from the behaviour of the linear polymer under the same conditions.

A bovine heparin fraction was examined by sedimentation analysis and intrinsic viscosity measurements as a function of ionic strength in the range of 0·1 to 1·0 M, and at pH 2·5 and 6·0. The following experimental parameters were obtained: M , S 0 20,W , D 0 20,W , V , and [η]. Other physical parameters were calculated based on a random coil model (supported by the theory of Mandelkern and Flory) e.g., ( r 2 ) 1 2 , ( s 2 ) 1 2 . Similar studies were made on a heparin sample as a function of desulphation as resulting from graded mild hydrolysis. Since desulphation is accompanied by decreasing anticoagulant activity of heparin, the latter was correlated with various calculated and measured physical parameters. Significantly ( r 2 ) 1 2 decreases with decreased desulphation and therefore decreased biological activity.

Dynamic thermogravimetric techniques (TG) have been utilized to estimate diffusion parameters during the desorption of water from Nylon 6 and Plexiglas films. Thus, values of activation energy of diffusion ( E D ) and diffusion constants ( D ) could be calculated from expressions derived for the estimation of these parameters from TG traces. In the case of Nylon 6, it was found that values of D were dependent upon heating rate (RH). Values of E D and D [(RH)→0] obtained were in reasonably good agreement with values reported from static (isothermal) measurements. Average values of E D (uncorrected) obtained for Nylon 6 and Plexiglas were, respectively, 7.0±0.4 and 10.7±1.2 kcal.mole −1 ; whereas, corresponding values of D [303°K and (RH)→0] were, 2.2 × 10 −9 and 2.9 × 10 −8 cm 2 .sec −1 . Advantages and limitations of the method employed are described.

Commercially prepared bovine heparin was fractionated by sequential elution from an ECTEOLA column into four discrete fractions and by solvent elution with an ethanol-water mixture into 12 fractions. Equilibrium centrifugation of the fractions in 0.5 m NaCl at pH 2.5 and interference optics revealed wide distribution of molecular weights. The fractions varied in biological activity and intrinsic viscosity. Chemical differences between fractions were minimal while the biological activity for the low molecular weight fractions were uniformly low. Inactivation with HCl, under mild conditions where biological activity was reduced fivefold, was not accompanied by reduction in intrinsic viscosity or molecular weight. A linear intrinsic viscosity-molecular weight relationship for the fractions prepared by alcohol elution can be described by the functions [η] = 1.75 × 10−5Mw0.98 in 0.1 m NaCl, pH 6.5, and [η] = 7.85 × 10−5Mw0.80 in 0.5 m NaCl, pH 2.5. An analogous relation for the sedimentation constant determined in 0.5 m NaCl at pH 2.5 was linear and described by s0 = 1.2 × 10−1Mw0.44. The data suggest that heparin in solution under the conditions studied exhibits substantial flexibility.

Commercial bovine heparin was fractionated by fractional precipitation, ethanol and dioxane were used as precipitants. The fractions varied in molecular weight from 4500 to 15,500. Cu (II) binding of the fractions was studied as a function of pH and biological activity. Cu (II) binding increases with increasing pH in the range examined (2.0–7.0), and increasing biological activity. The Cu (II) and biological activity as a function of molecular weight can be expressed by the relation 1 ϕ = a + b M , where ϕ is Cu (II) binding, or anticoagulant activity, M is molecular weight, and a and b are constants. Cu (II) binding involves the sulfate and carboxyl groups of heparin, which suggests the contribution of both to anticoagulant activity. The intrinsic viscosities of the fractions, at constant ionic strength, as a function of pH were also examined, including the relation to Cu (II) binding. Inactivation of heparin with HCl, under mild conditions where anticoagulant activity was reduced, was accompanied by reduction in (a) Cu (II) binding, (b) viscosity as measured in water, and (c) sulfation. The data suggest that the principal contributing factors of heparin as an anticoagulant are: (a) degree of dissociation of the ionizable groups, e.g., carboxyl, sulfate; and (b) molecular shape and size. Further, these factors contribute to the anticoagulant activity by virtue of their role in the binding process. Any outside forces that interfere with binding, such as pH, ionic strength, and hydrogen bonding, will affect the anticoagulant activity of heparin.

Commercial bovine heparin was fractionated by fractional precipitation using ethanol and dioxane as precipitating solvents. The fractions varied in molecular weight from 4500 to 15,500. The anticoagulant activity of the fractions increased with molecular weight up to about 10,000. However, the higher molecular weight fractions showed no appreciable difference in activity, which may be interpreted as a manifestation of sulfur heterogeneity. Several fractions having anomalous chemical, physical, and biological characteristics were also recovered. These fractions appear to be either of variable chemical composition or contain bound contaminants. The viscosity of heparin shows typical polyelectrolyte behavior. In water, the exponent (α) of the Mark-Houwink equation is 1.59. Although the value is below the theoretical limit of 1.8 for fully extended chains, comparison of the contour length of heparin with the end-to-end distance estimated from aqueous intrinsic viscosity data indicates that heparin is fully extended in water and suggests that heparin is probably an unbranched linear chain. In 0.01, 0.10, and 0.5 m NaCl, the α values are 1.13, 1.00, and 0.90, respectively, the latter representing the upper limit of the random coil. The variation of α under the conditions studied indicates that heparin is a substantially flexible chain.

The molecular weight and the radius of gyration of a fractionated sample of commercial bovine heparin were obtained using the method of low-angle X-ray scattering. The molecular weight of the heparin fraction was found to be 12,900 which is in excellent agreement with the values of 12,600 and 12,500 obtained for the same fraction from sedimentation equilibrium and viscosity measurements, respectively. A persistence length of 21.1 A and a radius of gyration of 35.9 A were calculated for the fraction. Under the experimental conditions studied (in water at room temperature) the heparin fraction may be described as a Gaussian coil molecule.

Graded self-hydrolysis of commercial bovine heparin produced samples of varying anticoagulant activity. The hydrolysis results in desulfation, which is accompanied by decrease in (a) sedimentation coefficient, (b) intrinsic viscosity when measured in water, and (c) axial ratios, a b , if a prolate ellipsoid model is assumed. Intrinsic viscosities obtained in 0.5 m NaCl were relatively unchanged for the hydrolyzed samples. The drop in molecular weight during inactivation is due to desulfation and not to depolymerization. Hydrolysis results in both O- and N-desulfation, the latter to a greater extent than the former. The data suggest that degree of sulfation and size and/or shape confer on heparin its biological activity.

Heat transfer effects during Teflon degradation by TGA were studied. Cylindrical samples were embedded in a thermal insulator so that only one of the faces was exposed. These insulated samples were then subjected to thermal degradation by means of TGA in a helium atmosphere. Above a Teflon-sample thickness of about 50–65 mils, a first-order plot afforded low values of activation energy ( E ) of 48–53 kcal·mole −1 . However, at higher conversions, values of E = 85–88 kcal·mole −1 obtained. When heat transfer effects were taken into account by the use of an appropriate equation, values of E = 86–88 kcal·mole −1 were obtained at the lower conversions. An insulated Teflon sample whose thickness was 27 mils afforded a value of E ≈ 77 kcal·mole −1 , based on a first-order plot, over a wide conversion range.

The kinetics of the thermal oxidation of isotactic poly(4-methyl-1-pentane) were studied in the bulk phase using thermogravimetric analysis (t.g.a.) at temperatures from 155° to 185°C and oxygen concentration from 75 to 100% by volume. The kinetics derived from formation of volatile products using t.g.a. correspond to those from non-volatile carbonyl products obtained from infra-red spectrometry.

A computer program (CP) is presented, based on a non-computer procedure reported in the literature for the determination of mechanism and corresponding activation energy utilizing non-isothermal TG data. This CP is then applied to six sets of TG data. The agreement between estimated and reported results is excellent. Various aspects and limitations of the CP are discussed.

In a previous communication [1], expressions were developed which were utilized to analyze data from non-isothermal TG (NITG) curves, at relatively low conversions, for activation energy (E). Such an analysis led to the estimation of E alone, virtually independent of reaction order (n) values. In this paper, expressions have been developed with the same goal in mind, to determine values of E irrespective of the n-values. To this end, rational approximations and an iterative computer procedure were employed.