Energy Fuels 2010, 24, 3028–3033 Published on Web 04/23/2010
: DOI:10.1021/ef100018j
Influence of the Alkane Molar Distribution on the Physical Properties of Synthetic Waxes D. Petitjean,*,† J. F. Schmitt,‡ V. Laine,† C. Cunat,‡ and M. Dirand† †
Laboratoire de Thermodynamique des Milieux Polyphas es, UPRES 3099, Ecole Nationale Sup erieure des Industries Chimiques, Institut National Polytechnique de Lorraine, Nancy University, 1 rue Granville, BP 451, 54001 Nancy Cedex, France, and ‡ Laboratoire d’Energ etique et de M ecanique Th eorique et Appliqu ee, UMR 7563, Ecole Nationale Sup erieure d’Electricit e et de M ecanique, Institut National Polytechnique de Lorraine, Nancy University, BP 160, 54504 Vandoeuvre-l es-Nancy, France Received January 18, 2010. Revised Manuscript Received April 2, 2010
The purpose of this paper is to compare the structure and the mechanical properties of several model mixtures exclusively constituted of pure linear alkanes so as to better understand the conditions in which disorder appears within real systems. The molar distribution of all the studied mixtures is of “normal logarithmic type”, and the only statistical parameter varying from one mixture to the other is the standard deviation (σ) of the distribution. This work was carried out by means of X-ray diffraction, differential scanning calorimetry (DSC), and dynamical mechanical analysis (DMA) according to temperature. The obtained results show that the number of crystallized phases increases with the standard deviation and that the structural evolution versus temperature of the mixtures also depends on this statistical parameter. With regard to the mechanical properties, the results of the dynamic mechanical analyses show that the storage modulus (E0 ) and the loss factor (tan δ) are also affected by the standard deviation of the distribution.
mixtures to be deduced. More recently, studies relative to normal alkane mixtures were performed. Two cases are distinguished according to the shape of the alkane molar distribution.13 Thus, a single solution with an orthorhombic structure is detected in the case of mixtures for which the distribution is “normal logarithmic”.14-16 On the contrary, mixtures with an exponential decreasing distribution can form several solid solutions with an orthorhombic structure.13,17,18 Whatever is the distribution, these orthorhombic phases (generally noted β0 ) are isostructural to the intermediate phases previously identified in the binary or ternary molecular alloys.9,11,12 All these solid solutions evolve via several solidsolid transitions by increasing temperature before melting. The high temperature phases are well described in the following references.6,7,13 Few papers19-25 deal with the effect of the composition and structure on the degree of crystallinity of waxes. A certain
Introduction In recent years, it has become very important to improve the knowledge of the relatively high-molecular-weight hydrocarbons contained in petroleum cuts. In fact, these compounds present many industrial applications when they are mixed. So, their properties, which are sensitive to temperature and tied to their structural state, must be well-known. Thus, studies relative to alkanes and their mixtures must be correlated to structural characterization. Since the first characterization made by Muller and Saville in 1925,1 many works have been published on the subject2-5 as structural analyses at various temperatures performed to establish binary-6-10 or ternary-phase diagrams.11,12 Such representations allow much information on the binary and ternary *To whom correspondence should be addressed. E-mail: dominique.
[email protected]. (1) Muller, A.; Saville, W. B. J. Chem. Soc. 1925, 127, 599. (2) Craig, S. R.; Hastie, G. P.; Roberts, K.; Sherwood, J. N. J. Mater Chem. 1994, 4 (6), 977. (3) Gerson, A. R.; Roberts, K. J.; Sherwood, J. N. Acta Crystallogr. 1984, B47, 280. (4) Heyding, R. D.; Russel, K. E.; Varty, T. L. Powder Diffr. 1990, 5 (2), 93. (5) Turner, W. R. Ind. Eng. Res. Dev. 1971, 10 (3), 238. (6) L€ uth, H.; Nyburg, S. C.; Robinson, P. M.; Scott, H. G. Mol. Cryst. Liq. Cryst. 1974, 27, 337. (7) Achour-Boujema, Z.; Bourdet, J. B.; Petitjean, D.; Dirand, M. J. Mol. Struct. 1995, 354, 197. (8) Denicol o, I.; Craievich, A. F.; Doucet, J. J. Chem. Phys. 1984, 80, 6200. (9) Dirand, M.; Achour, Z.; Jouti, B.; Sabour, A.; Gachon, J. C. Mol. Cryst. Liq. Cryst. 1996, 275, 293. (10) Metivaud, V.; Rajabalee, F.; Mondieig, D.; Haget, Y. Chem. Mater. 1999, 11, 117. (11) Nouar, H.; Petitjean, D.; Bouroukba, M.; Dirand, M. Rev. Inst. Fr. Pet. 1998, 53, 21. (12) Nouar, H.; Petitjean, D.; Bouroukba, M.; Dirand, M. Mol. Cryst. Liq. Cryst. 1999, 326, 381. r 2010 American Chemical Society
(13) Dirand, M.; Bouroukba, M.; Chevallier, V.; Petitjean, D. J. Chem. Eng. Data 2002, 47, 1255. (14) Chevallier, V.; Provost, E.; Bourdet, J. B.; Bouroukba, M.; Petitjean, D.; Dirand, M. Polymer 1999, 40, 2121. (15) Chevallier, V.; Petitjean, D.; Ruffier-Meray, V.; Dirand, M. Polymer 1999, 40, 5953. (16) Rakotosoana, A. R.; Bouroukba, M.; Petitjean, D.; Dirand, M. Energy Fuels 2008, 22, 784. (17) Briard, A. J.; Bouroukba, M.; Petitjean, D.; Hubert, N.; Moı¨ se, J. C.; Dirand, M. Fuel 2005, 84, 1066. (18) Briard, A. J.; Bouroukba, M.; Petitjean, D.; Hubert, N.; Moı¨ se, J. C.; Dirand, M. Fuel 2006, 85, 764. (19) Dirand, M.; Chevallier, V.; Provost, E.; Bouroukba, M.; Petitjean, D. Fuel 1998, 77, 1253. (20) Dorset, D. L. J. Phys. D: Appl. Phys. 1997, 30, 451. (21) Le Roux, J. H. J. Appl. Chem. 1969, 19, 39. (22) Retief, J. J.; Le Roux, J. H. S. Afr. J. Sci. 1983, 79, 234. (23) Basson, I.; Reynhardt, E. C. Chem. Phys. Lett. 1992, 198, 367. (24) Le Roux, J. H. J. Appl. Chem. 1969, 19, 203. (25) Petitjean, D.; Schmitt, J. F.; Laine, V.; Bouroukba, M.; Cunat, C.; Dirand, M. Energy Fuels 2008, 22, 697.
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degree of amorphousness in some waxes is reported in the literature,19 due to the presence of long “tie” molecules in natural waxes, which lead to a conformational disorder near the chain ends.20 In the case of real mixtures, oil content, isoparaffins, and branched chains play probably a significant role in the disorder.21-24 The influence of the composition and especially the isoalkane amount in the wax was particularly studied and presented in a previous paper.25 To better understand the conditions in which the disorder appears within real waxes and especially the influence of the alkane distribution, synthetic mixtures exclusively composed of linear alkanes were studied. Their distribution is “normal logarithmic” and close to that of the oil refining products. The only varying parameter from one mixture to other is the width of the distribution, so the root-mean-square deviation from the mean of the Gaussian distribution (σ). In this paper, we present original results about the influence of the statistical parameter σ on the disorder appearance, the structure, and the mechanical properties. This work was essentially carried out by means of X-ray diffraction, differential thermal analysis (differential scanning calorimetry), and dynamic mechanical analysis for measurement of the storage modulus (E0 ) and of the loss factor (tan(δ)) according temperature.26
Table 1. Characteristics of the Synthetic Mixtures synthetic mixture
composition in normal alkanes
percent in normal alkanes
μ
σ
S1.5 S3 S4.4 S5.8
C24H50 to C35H72 C20H42 to C40H82 C18H38 to C42H86 C18H38 to C42H86
100 100 100 100
29.5 29.5 29.5 29.6
1.5 3.0 4.4 5.8
Experimental Section Many synthetic mixtures of consecutive n-alkanes were prepared for this study. Each synthetic wax has a Gaussian distribution of n-alkane molar fractions determined according to the following relation: " #2 1 1 ci - μ Xi ¼ pffiffiffiffiffiffi exp 2 σ σ 2π with Xi the molar fraction of the i n-alkane, ci its carbon atoms number, μ the average number of carbon atoms of the distribution, and σ its standard deviation. The molar fractions of the n-alkanes were calculated from μ and σ taking into account the following conditions: we avoided choosing an integer for the value of μ so that this one is not identical to that of a pure normal alkane. Furthermore, such a choice is in good agreement with the fact that the value of μ is not generally whole in the case of real mixtures. Given that the structural behavior of alkanes for which the carbon atom number is included between 25 and 30 is well-known, we decided that the whole part of μ must be odd and included between these two values (we chose an odd number in order to have an orthorhombic system for each mixture).26 Finally, the value of μ must be compatible with the available pure alkanes (from octacosane C18H38 to dotretacontane C42H86). Taking into account all these criteria, the adopted value for μ was 29.5. The synthetic mixtures noted (Sσ) (where σ is the standard deviation of the distribution) were prepared by weighting, mixing, and melting pure alkanes (from C18H38 to C42H86) together. Solid samples were obtained after cooling to ambient temperature. Their aspect was that of a whitish wax. The pure components were purchased from the Fluka Company, and purities were greater than 97% (as indicated in the catalog). Some statistical properties of synthetic mixtures which have a characteristic thermal behavior are collected in Table 1 and Figure 1. The exact compositions of these waxes can be obtained in ref 26. All the mixtures were analyzed by X-ray diffraction so as to determine their structural state. The X-ray diffractometer used in this study was previously described.25-27 We only remind readers
Figure 1. Molar distributions in the synthetic mixtures S1.5, S3, S4.4, and S5.8 (μ = 29.5).
here that the apparatus uses the copper radiation λKR Cu and is equipped with a curved detector (CPS 120°), allowing the recording of the diffracted X-ray beam in the large angle range. A heating sample holder based on the Peltier effect makes possible the identification of structural modifications from room temperature to near 373 K. The preliminary protocol was the following one: the sample was heated to the melting point and then cooled slowly
(26) Laine, V. Ph D Thesis, Institut National Polytechnique de Lorraine (INPL), Nancy, France, 2005. (27) Petitjean, D.; Schmitt, J. F.; Fiorani, J. M.; Laine, V.; Bouroukba, M.; Dirand, M.; Cunat, C. Fuel 2006, 85, 1323.
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Table 2. Characteristics of the DMA Experiments applied solicitation imposed dynamic displacement sample shape and dimensions glue frequency specimen holders range of explored temperature heating speed
Table 3. Structure and Crystallographic Parameters of the Synthetic Waxes
tension/compression 3 μm cylinder length l = 8 mm; diameter Φ = 4 mm M-BOND 200 Adhesive 10 Hz parallel plates from room temperature to fusion temperature 0.5 K 3 min-1
synthetic mixture S1.5 S3 S4.4 S5.8
at 1 K 3 min-1 on a copper sheet until reaching room temperature. Such a protocol allows preferential crystallographic orientations to be obtained (the molecular chains are perpendicular to the sample holder), and therefore the relative intensities of the reflections (00l) are increased artificially. In such conditions, it was easy to count the phases and to calculate the crystallographic parameter c with good accuracy. Furthermore, the examination of the sample as powder according to a transmission method allowed not only the crystallographic parameters a and b to be evaluated but also the proportion of the diffusion halo, characteristic of the presence of an amorphous phase, to be estimated. Dynamic mechanical analyses (DMA) were carried out to study the thermomechanical behavior of the mixtures (Sσ). A METRAVIB viscoanalyzer (type VA 2000) was used for these experiments: the apparatus and the experimental protocol were described in detail in a previous paper,27 and we give only here the main characteristics of the experiments. The tension/compression test mode was used, and the parallel plates specimen holder was chosen because it is the most adapted to the tested products. The samples (small cylinders) are stuck between the parallel plates. An electromechanical shaker imposes a well controlled sinusoidal displacement at the superior extremity of the sample, and a transducer force measures the transmitted force, also in terms of phase and peak amplitude. The complex stiffness K* is accessible from the ratio force/displacement. Calculations make it possible to evaluate the complex modulus E* of the material using a shape factor (this shape factor takes into account the geometry of the sample and the solicitation).28 We remind readers that E* can be written: E*=E0 þ jE00 , where E0 is the storage modulus and E00 the loss modulus. The ratio E00 /E0 =tan δ is the loss factor: it is proportional to the ratio of energy lost to energy stored in one cycle. The characteristics of the DMA experiments are presented in Table 2.
phase
a (nm)
b (nm)
c (nm)
nRX
Δn = nRX - μ
β0 β0 β0 β0 I β0 II β0 III
0.487 0.488 0.487 0.487
0.739 0.739 0.738 0.740
7.911 8.037 8.298 7.425 8.465 9.813
29.5 30.1 31.2 27.7 31.8 37.1
0 0.6 1.7 -2 2.1 7.4
from the (00l) diffraction peaks and more precisely from the interplanar distances d00l calculated using Bragg’s law. The values so obtained reveal that c is dependent on σ: c increases with σ in the case of single solid solutions (for values of σ included between 1.5 and 4.4, see Table 3). Furthermore, nRX can be calculated with the help of the following relation:13-15 nRX ¼
cðnmÞ - 0:3750 0:2544
This carbon atom number is then compared with the average carbon atom number of the mixture Sσ. The phase number, the structure type, and the crystallographic parameters of the synthetic waxes Sσ appear in the Table 3. When the wax presents a single phase, the difference Δn=nRX - μ reveals an excess of the carbon atom number attributed to the conformational disorder. In the case of the mixture S1.5, this excess value equal to 0 indicates a good agreement with the weak dispersion of the alkanes; this mixture can be likened to a hypothetical pure alkane of formula CμH2 μþ2 with μ equal to the average carbon atom number of the mixture. This result is in good agreement with previous works.13-15,22,29-32 In the case of the mixtures S3 and S4.5, the excess value increases with σ: this reveals the presence of a disorder increasing with the dispersion of the distribution. At ambient, the mixture S5.8 stabilizes three solid solutions: two phases for which the average carbon atom numbers are equal to 31.8 and 37.1 and a lighter phase for which the average number is lower than that determined by the statistics (Δn=-2). The ratio of the amorphous phase was evaluated by a deconvolution procedure.26 This ratio can be written as follows:
Results and Discussion
%amorphous ¼ 100
All the mixtures were analyzed by X-ray diffraction at room temperature according to a transmission method. The patterns reveal that all the waxes (Sσ) crystallize in the orthorhombic system characterized by the Bragg diffraction peaks (110/111) and (020/021) and by the homologue series of (00l) reflections. The studied mixtures thus form solid solutions, isostructural to the ordered intermediate phase (noted β0 ) previously identified and characterized with binary6-10 or ternary11,12 alloys of linear alkanes. The evaluation of the hkl interplanar distances from the diffractograms allows the crystallographic parameters a and b of the solid solutions to be calculated (Table 3). The obtained values are constant whatever the standard deviation σ and are in good agreement with those previously reported in the literature in the case of pure alkanes with orthorhombic structure.2 The parameter c is correlated to the length of the molecular chain of a hypothetical linear alkane representative of the solid solution and, therefore, to an average carbon atoms number (nRX). It is determined
Ahalo Ahalo þ Apeaks
where Ahalo is the area of the Gaussian function characteristic of the amorphous fraction and Apeaks the area of the Gaussian function characteristic of the crystalline function (the sum of the areas of peaks (110)/(111) and (020)/(021)). The percentages of amorphous phase so calculated are collected in Table 4. Examination of the data shows that the amount of amorphous phase varies from 11.3 (for S1.5) to 40.4% (for S5.8) and increases with the standard deviation σ. Such results confirm the previous ones (qualitative analysis of the diffractograms) and show that the observed disorder is only induced by the dispersion of the alkanes distribution (standard deviation σ). (29) Chevallier, V.; Provost, E.; Bourdet, J. B.; Bouroukba, M.; Petitjean, D.; Dirand, M. Polymer 1998, 40 (8), 2121. (30) Chevallier, V.; Briard, A. J.; Petitjean, D.; Hubert, N.; Bouroukba, M.; Dirand, M. Mol. Cryst. Liq. Cryst. Sci. and Tech. (Section A) 2000, 350, 273. (31) Chevallier, V.; Petitjean, D.; Bouroukba, M.; Dirand, M. Polymer 1998, 40 (8), 2129. (32) Craig, S. R.; Hastie, G. P.; Roberts, K. J.; Sherwood, J. N.; Tack, R. D.; Cernik, R. J. J. Mater. Chem. 1999, 9 (10), 2385.
(28) Greif, R.; Johnson, M. S. J. Eng. Mater. Technol. 1992, 114, 77.
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Table 4. Percentage of Amorphous Phase in the Synthetic Waxes Sσ synthetic wax
percent of amorphous phase
S1.5 S3 S4.4 S5.8
11.3 24.3 31.9 40.4
Table 5. Solid-Solid Transitions of the Synthetic Mixtures S1.5, S3, S4.4, and S5.8a
a
The temperatures of transition are given in brackets.
So, the statistical parameters seem to have the same incidence as the composition (presence of isoalkanes notably25) on the structural state. As it was previously described,7,13-15,25,27 increasing temperature induces important structural modifications. The structural evolution of each wax versus temperature highly depends on σ (Table 5). As indicated in the literature, the orthorhombic solid solution evolves via several solid-solid transitions before melting. The structural evolutions of the waxes S1.5 and S3 are similar to that of binary solid solutions. The first transition transforms the ordered phase β0 into a disordered phase called β(Fmmm). Then the increase of the temperature provokes the disorder/disorder transition corresponding to the transformation of this phase into the rotator phase R-RII.6 In the case of the wax S4.4, a second solid solution, isostructural to the ordered intermediate phase β0 , is detected at low temperatures. Only one solid-solid transition is then observed before melting, transforming the phase β0 into the disordered phase R-RII. As for the wax S5.8, no solidsolid transition is detected and only the three crystallized phases formed at ambient disappear successively. Figure 2 illustrates the incidence of the standard deviation on the thermograms recorded by DSC. All the mixtures (Sσ) were studied by dynamic mechanical analyses. We present the evolution of the storage modulus (E0 ) and that of the loss factor (tan δ) versus temperature on every figure. The loss factor (tan δ) reports the dissipation and presents the advantage of being independent from the geometry of the samples. The domains of stability in temperature of the various phases deducted from structural and calorimetric data were systematically put back. The results obtained for the mixtures S1.5, S3, S4.4, and S5.8 presenting an increasing content in amorphous phase are given in Figures 3-6. In the case of the mixture S1.5, the obtained results reveal that the mechanical behavior is well correlated to the structural evolution versus temperature (Figure 3). From ambient temperature
Figure 2. Thermograms of the mixtures S1.5, S3, and S4.4 (recorded by DSC).
Figure 3. Evolution of the storage modulus (E0 ) and of the loss factor (tan δ) versus temperature in the case of the mixture S1.5.
to 328 K, E0 is appreciably constant as well as tan δ, whose values remain weak. According to the structural analyses, this 3031
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ting movement whose amplitude increases gradually with temperature, then to the appearance of the rotator phase R-RII in which molecules are in rotation around their molecular axis.13 In the temperature range 331-334 K, the step recorded for E0 corresponds with the stabilization of the rotator phase R-RII. E0 is then equal to approximately 6 MPa. A neighboring value has been obtained for the same phase in the case of a commercial wax studied in a previous paper.27 Finally, as it was observed for pure alkanes,27 a decrease of the modulus E0 and a significant increase of the loss factor tan δ recorded from 334 K are characteristic of the approach of the fusion. Such evolutions are observed for all the mixtures (Figures 3-6). The curves obtained for S3 show that the presence of amorphous phase in a more important quantity has an incidence on the mechanical behavior of the mixture (Figure 4). Indeed, contrary to S1.5, a decrease of E0 can be detected from the beginning of the experiment until the temperature of 320 K (from approximately 1000 to 400 MPa): this domain is characteristic of the ordered phase β0 . From 320 to 329 K, a decrease of the storage modulus is recorded corresponding to the transformation of the ordered low temperature phase into the disordered high temperature phase R-RII. The fact that the decrease occurs during 9 K instead of 3 K for S1.5 can be correlated to the width of the endotherm of the solid/solid transition corresponding to the disorder within the mixture. A step characteristic of the domain where R-RII exists is then detected: the domain is wider than previously but the value obtained for E0 is again equal to some megapascal. Finally the abrupt decrease of E0 indicates the beginning of the fusion. The regular increase of tan δ from ambient probably also indicates the high disorder of the mixture. As concerns the mixture S4.4 (Figure 5), the decrease of the modulus E0 presents a break of hillside in the neighborhood of 325 K due to the solid order/disorder transition identified by X-ray diffraction and calorimetry (a decrease of one decade is recorded on a weak temperature range). As for S3, the continuous increase of tan δ from the beginning of the heating corresponds with the high amorphous phase content. The phase R-RII is also characterized by a step at approximately 2 MPa between 329 and 334 K. Finally, the evolution of E0 and tan δ recorded for the mixture (S5.8) are in good agreement with the absence of solid/solid transition (Figure 6): E0 decreases and tan δ increases continuously without any singularity (no local maximum for tan δ). These results keep pace with the consumption of enthalpy recorded by calorimetry and thus with the disorder inherent to the mixture. So the results of the thermomechanical study clearly show that the mechanical behavior of paraffin wax is strictly connected to its structural state and to the presence (or the absence) of solid/solid transitions. The steps of the curve E0 = f(T) tend to disappear as the disorder increases for the benefit of a regular decrease without break of hillside. The values obtained for the storage modulus of the low temperature phase are dependent on the amorphous content of the mixture. On the contrary, they are always equal to some megapascal for R-RII (when this phase exists).
Figure 4. Evolution of E0 and tan δ versus temperature in the case of the mixture S3.
Figure 5. Evolution of E0 and tan δ versus temperature in the case of the mixture S4.4.
Figure 6. Evolution of E0 and tan δ versus temperature in the case of the mixture S5.8.
domain corresponds to the stabilization of the low temperature phase β0 of the orthorhombic structure. In this state, the rigidity of the material is maximal and the value of the storage modulus is around 300 MPa. This value is in good agreement with those obtained for pure alkanes such as C24H50 for instance.27 From 328 K, a decrease of E0 is detected on a restricted temperature domain: this rapid decrease can be correlated to the transition transforming the ordered phase β0 into the disordered phase β(Fmmm). In the same temperature range, tan δ increases and seems to present two local maxima at 329 and 331 K which can be correlated to the consumption of enthalpy due to the order/disorder transitions observed by calorimetry. From a mechanical point of view, this transition area is characterized by a loss of rigidity: this phenomenon is due at first to the rotator state I (β-RI) of the disordered phase β(Fmmm) in which molecules are animated by an oscilla
Summary and Conclusion In this paper, we try to determine the effect of the distribution in n-alkanes of synthetic mixtures on their structural state and mechanical properties by means of X-ray diffraction, DTA, and DMA. We remind readers that the molar distribution of the mixtures is of “normal logarithmic type”, and we 3032
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study particularly here the influence of the standard deviation σ. At ambient, we show that the number of crystallized phases increases according to the standard deviation. A single solid solution of orthorhombic structure (β0 ) is detected for weak standard deviations (S1.5, S3, S4.4) while several phases are detected in the case of higher standard deviations (mixture S5.8, for instance). This last result differs from those previously obtained in the case of real mixtures containing other hydrocarbons.33 It seems that the presence of other hydrocarbons in real mixtures promotes the formation of a single solid solution or prevents the appearance of other solid solutions by forming a more important amorphous phase composed by linear and nonlinear alkanes. The structural evolution versus temperature
also depends on the standard deviation. While the mixtures S1.5 and S3 evolve as the binary solid solutions β0 , a second phase appears at low temperature leading to the formation of a second isostructural solid solution, and a single solid/ solid transition is detected before melting. For higher standard deviations (S5.8, for instance), no transition is detected and the successive disappearance of the phases crystallized at ambiant is observed. Finally, all the results of the thermomechanical study clearly show that the mechanical behavior of the synthetic mixtures is strictly connected to their structural state at ambient and to the number of solid/ solid transitions versus temperature. The modules’ evolution is very sensitive to the standard deviation and thus to the disorder. The decrease of the storage modulus by stages tends to disappear and to become continuous as the disorder increases.
(33) Pierre-Brice, M. Ph.D. Thesis, Institut National Polytechnique de Lorraine (INPL), Nancy, France, 2002.
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