WAXS and Turbidity Studies of the Structure and

In-Situ SAXS/WAXS and Turbidity Studies of the Structure and Composition of Multihomologous n-Alkane Waxes Crystallized in the Absence and Presence of Flow Improving Additive Species

CRYSTAL GROWTH & DESIGN 2004 VOL. 4, NO. 5 1069-1078

Alison Hennessy,*,† Anne Neville,‡ and Kevin J. Roberts§ School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, Scotland, UK, School of Mechanical Engineering, University of Leeds, Leeds LS2 9JT, UK, and Institute of Particle Science and Engineering, Department of Chemical Engineering, University of Leeds, Leeds LS2 9JT, UK Received June 24, 2003;

Revised Manuscript Received January 16, 2004

ABSTRACT: Wax deposition on engineering components can cause severe operational problems in oil recovery. These problems are examined through a study focused on understanding the mediating role played by the chemical inhibitors that are commonly used to prevent or delay the wax crystallization process. Solution crystallization data from homologous mixtures of n-alkanes, as measured via optical turbidometric methods and in-situ combined small and wide-angle X-ray scattering (SAXS/WAXS) techniques, reveal a direct correlation between the type and concentration of polymeric additive used and the resultant crystallization behavior. The behavior of additives, such as polar macromolecules with nonpolar alkyl chains protruding from the backbone, was consistent with their binding within the basal plane of the wax crystal structure, associated with intermolecular (alkane/additive) interactions of an epitaxial nature. Overall, the results were consistent with a number of structurally related factors influencing the additive-mediated wax crystallization process. The c-axis of the additive-mediated crystallized wax was found to be related to the longest chain in the homologous wax mixture, the a and b axes were determined by the inhibitor family used, and the inhibitor efficiencies were determined by the chain lengths of the alkyl chains protruding from the inhibitor backbone. 1. Introduction The presence of crystallized wax in crude oil under cold flow conditions has hindered efficient oil transport since oil production began. Wax deposits can be found to occur on the well casing perforations, screens, and pumps, and most significantly on the pipeline walls.1 Petroleum waxes that contain high proportions of nalkanes exhibit crystal morphologies and crystallographic structures very similar to those known for the pure n-alkanes. The individual components of a homologous series of n-alkane waxes are compatible with each other, thus permitting easy cocrystallization behavior. They can also tolerate small amounts of other types of hydrocarbons without drastically differing the observed crystal habit typically observed in pure n-alkanes. Multihomologue petroleum waxes commonly crystallize in an orthorhombic structure similar to that adopted for pure n-alkanes with an odd parity of carbons.2 Because of their intrinsic simplicity, chemical inhibitors are the most desirable way to prevent wax crystallization in practical pipeline systems; however, while it is clear that these additives do work, the mechanisms underpinning their action remain unclear at the present time. Most wax inhibitors possess a polar backbone and * To whom correspondence should be addressed. Current address: Department of Dermatology, Royal Infirmary of Edinburgh, Edinburgh University, Edinburgh EH3 9YW, UK. E-mail: alison.hennessy@ ed.ac.uk. † Heriot-Watt University. ‡ School of Mechanical Engineering, University of Leeds. § Institute of Particle Science and Engineering, Department of Chemical Engineering, University of Leeds.

alkyl side chains, and several authors have reported a correlation between inhibitor alkyl chain length and wax chain length.3-5 In 1967, Chichakli and Jessen observed fractional crystallization, where long chain n-alkanes in a homologous mixture crystallized before the shorter chain alkanes in an additive-mediated solution. They suggested that the additive slowed the crystallization process, which would allow longer homologues to crystallize first.6 Ding et al7 presented a detailed thermodynamic analysis for the interaction of polyacrylate with a wax mixture in heptane. These workers used the crystallization temperature of the wax as a measure of its solubility in heptane. Their estimations of thermodynamic changes showed a decrease in both the entropy and enthalpy changes of the system in the presence of inhibitor. This supports the intuitive result that the presence of inhibitor increases the disorder in a wax crystal. Using transmission electron microscopy (TEM) they observed a vesicle, or loop of inhibitor, which, on addition of wax, retained its shape but increased in thickness as the wax cocrystallized with the inhibitor. A correlation between c-axis length and average carbon number has been observed by several workers.8 Previous work by Craig et al.9 summarized in Figure 1 shows this correlation for diesel wax, revealing the relationship between c-axis length and alkyl chain average carbon number to be approximately linear. This work was supported by previous FTIR studies10 in which incipient chain folding was proposed as an explanation for the deviations in the expected trend. Orthorhombic n-alkane unit cells contain four molecules and the steric

10.1021/cg0341050 CCC: $27.50 © 2004 American Chemical Society Published on Web 04/17/2004

1070 Crystal Growth & Design, Vol. 4, No. 5, 2004

Hennessy et al.

Figure 1. Graph correlating the calculated c-axis lengths of the wax crystals with their average carbon number. wax (provided by BP), 90% decane, and 5% toluene. This repulsions between the terminal methyl groups mainmixture was used to accurately represent the main constitutain an interlamellar distance between end groups. Craig ents of crude oil, with the addition of the more polar toluene suggested that chains fold back into the same lamella enabling inhibitor solubility. The wax component was provided in a similar way to infinite chain polyethylenes.9 This by a model wax which is a homologous mixture of n-alkanes 11 view was supported by Dirand et al who confirmed possessing carbon chains ranging from 21 to 33 carbons, with that homologous mixtures of n-alkanes crystallized in an average carbon chain length of 27.6 carbons. Figure 2 shows an orthorhombic phase with a c-axis corresponding to the relative composition distribution of the wax with respect to n-alkane chain length as determined using gas chromatoga value slightly larger than the medium carbon atom raphy. For reference purposes, two pure single n-alkanes were in the mix. They attributed this slight excess to the also examined: C27H56 (heptacosane) and C28H58 (octacosane) steric interlamellar disorder caused by chain bending. being representative15 of n-alkanes having orthorhombic and 12 Dorset however disagreed with this and used singlemonoclinic crystallographic structures, respectively. The comcrystal analysis to support his theory that the longer puter program Dragon16 was used to obtain all the reflections homologues are accommodated within the unit cell by for heptacosane. Dragon is a computational tool used to yield X-ray diffraction peak positions when the unit cell is known. longitudinal translational disorder. Work by Gerson et al.13 has also, to some degree, supported the view that Two commercial additive types were examined, both of which were based on a comb polymer structure, varying in the longer n-alkanes penetrated adjacent layers. terms of the chain length of the protruding alkyl chain. The More recent work has been carried out by Chevallier additives were provided by BP; their full chemical details and 14 et al who used X-ray diffraction to monitor the formulas are currently commercially confidential and hence crystallized phases from a multiparaffinic wax on coolhave not yet been published in the open literature. Hereafter, ing. Their first deposits contained a single solid solution. these are referred to as inhibitor families 1 and 2, with the The composition of this single phase altered slightly on former being based on substituted poly alkyl esters and the latter being based on substituted alkylated polyethylene cooling, with a contraction of the c-axis length with the imines. The alkyl tails in inhibitor 1 had chain lengths of 16, incorporation of increased numbers of shorter homo18, 20, and 22 carbons, while those in inhibitor 2 have alkyl logues. These findings were supported by gas chromachain lengths of 16, 20-24, 24-28, and >30 carbons, respectography. tively. For identification purposes, the chain length of the An increased understanding of the mechanistic and individual additive species are identified here in parentheses, kinetic action of current cold flow additives on wax e.g., inhibitor 1 (18). crystallization is clearly a prerequisite to the design of 2.2. Experimental Techniques. The metastable zone the next generation of inhibitor species. This perspective width (MSZW), i.e., the difference between the crystallization (Tcryst) and dissolution (Tdiss) on-set temperatures, was measets the scene for this paper, which describes an sured using an automated apparatus17-20 to characterize the examination of multihomologous wax crystal deposition bulk precipitation characteristics of wax/inhibitor solutions from a model hydrocarbon solvent examined in the (Figure 3). The nucleation apparatus utilized a sealed glass absence and presence of a number of additive species. vessel containing a wax/inhibitor/solvent fraction, which was In this work, optical turbidometric methods were used constantly agitated using a magnetic stirrer and flea and to measure the crystallization and dissolution temperplaced within a temperature-controlled water bath. As the atures, and combined small and wide-angle X-ray scattemperature of the bath was lowered, the onset of nucleation was detected by measuring the change in transmittance of tering (SAXS/WAXS) was used to assess changes to the light using a turbidity probe and conversely the crystal wax crystal structure during the solution cooling crysdissolution temperature following reheating. The values of tallization process. Tcryst and Tdiss for a crystallizing solution in the absence and presence of 400 ppm inhibitor were determined at four 2. Materials and Methods predefined temperature-programmed cooling/heating rates: 0.75. 0.5, 0.25, and 0.1 °C/min, with the tests being repeated 2.1. Materials. The base waxing medium used for the three times to check reproducibility. Extrapolation of the data majority of the experiments was a model oil comprising 5%

Multihomologous n-Alkane Waxes

Crystal Growth & Design, Vol. 4, No. 5, 2004 1071

Figure 2. Gas chromatograph showing the percentage distribution of n-alkanes in the model oil used in this study. 10 to 57° 2θ. For the SAXS detector, a vacuum chamber between the sample and detector was used to eliminate air scattering. Rat tail collagen and polyethylene were used respectively to calibrate the SAXS and WAXS detectors. The samples examined in this in-situ crystallization part of the study were a 10% model oil, and 800 ppm Inhibitor 1 (16), Inhibitor 1 (2), and Inhibitor 2 (16) mediated model oil. These relatively higher concentrations were required, reflecting the fact that there might not be sufficient X-ray scattering with the more dilute 5% model oil. The solutions were examined using the flow cell shown in Figure 5. In this, saturated solution fed from a ca. 100 mL temperaturecontrolled glass jacketed vessel was pumped at a constant rate of 66 mL/min (to ensure thorough mixing) through the WAXS/ SAXS brass jacketed cell and back to the feed vessel via a continuous flow loop. The in situ cell contained a pair of thin X-ray transparent mica windows, through which the synchrotron beam could pass. This system allowed effective in-situ monitoring of the crystallization of wax under well-controlled thermal conditions.

3. Results

Figure 3. Schematic diagram showing the basic features of the automated turbidometry apparatus as used for determination of the kinetics of precipitation from bulk solution. to zero cooling rate enabled determination of the MSZW under limiting, or equilibrium conditions. Figure 4 shows a turbidity plot for the model wax, cooled and heated at 0.1 °C/min, showing representative results from the cooling and heating cycles, as well as the points used to determine Tcryst and Tdiss. X-ray scattering was used to monitor the crystalline characteristics of wax as it formed in the absence and presence of inhibitor. A laboratory Siemens D500 flat-plate diffractometer was used to identify the 2θ range of interest for subsequent examination using the more high-intensity synchrotron radiation facilities needed for the in-situ studies. For the latter, station 8.2 at the Daresbury Synthetic Radiation Facility (SRS) was used to collect wide angle and small-angle X-ray scattering data (WAXS and SAXS) of wax crystal samples during crystallization. This facility was setup for these experiments using a linear quadrant SAXS detector, located 3m from the sample cell covering the angular scattering range from 0 to 3° 2θ together with a WAXS detector (INEL CPS120), located 222 mm from the sample covering the broader angular range from

The crystallization temperature, dissolution temperature, and the MSZW of the model wax and each of the inhibited solutions studied were determined using the automated temperature-programmed turbidometry apparatus. Figures 6-8 show turbidity plots for three additivemediated wax solutions cooled and heated at 0.1 °C/min. The wax reference with no inhibitor is plotted with a solid line. Figure 9 is a comparison between the crystallization temperatures and MSZW for each of the additive-mediated solutions. Inhibitor 1 (20), Inhibitor 1 (22), and Inhibitor 2 (20-24) showed a marked initial decrease in transmittance of light at a relatively high temperature, which then stabilized until the temperature was lowered and a second sharp decrease occurred. This effect was also observed to a lesser extent for Inhibitor 1 (16), Inhibitor 2 (24-28), and Inhibitor 2 (>30). This profile is consistent with fractional crystallization within the multihomologous wax mixture. The initial fraction of the multihomologous wax crystallized would be richer in the longer chain components, reflecting their lower solubility with respect to the shorter


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Figure 4. The turbidity plot for a model wax solution cooled at 0.1 °C/min, showing Tcryst and Tdiss.

character with the sharp peaks illustrating crystallinity and long-range order with the broader background humps being due to diffuse scatter reflecting sample disorder and possible solvent incorporation. Figure 11 is an example of the SAXS/WAXS time-resolved plots, and shows the model wax formed in the presence of 800 ppm Inhibitor 1 (22). Drawing on our previous paper characterizing n-alkane crystallograph and the measured WAXS data, the values for the lattice parameters a, b, and c were calculated for each of the samples examined. The position of the amorphous halo, obtained from the WAXS data, is also noted. These values are given in Table 2 along with the known lattice parameters for C29H60, C31H64, and C33H68. The ratio of b/a provides information on whether an n-alkane is crystallizing in the low temperature or rotator phase orthorhombic system, i.e., values of 1.5 and x3 being indicative of the low temperature and hexagonal rotator phases, respectively.24 4. Discussion Figure 5. Schematic diagram of the in-situ flow cell used in the WAXS/SAXS experiments.

chain components. Presumably, the changing solution composition downstream of the initial crystallization produced supersaturation with respect to the lower molecular weight species; this would initiate the crystallization of a wax with a different crystallographic phase and hence solubility and metastable zone width. In the case of the remaining inhibitors, hysteresis was sharp with only a single onset point being observed. Table 1 gives the numerical values for the MSZW and crystallization temperatures for each of the samples examined. Two values of MSZW are given for Inhibitor 1 (22) and Inhibitor 1 (20), reflecting the double peaks observed in the temperature cycle hystereses profile. Figure 10 shows a powder XRD pattern of the model wax, revealing evidence for both crystalline and diffuse

4.1. Analysis of the Turbidometric Data. In the Inhibitor 1 family, addition of inhibitor invariably increased the size of the MSZW compared with the solution containing wax alone. As the chain length of the inhibitor tail increased from 16 carbons (Inhibitor 1 (16)) to 22 carbons (Inhibitor 1 (22)), the crystallization temperature increased until it was similar to that of the model oil, which contained n-alkanes ranging from 22 to 33 carbons. While literature reports have concluded that the inhibitor/alkane interactions are greatest when their chain lengths match,3-5 most of these studies have been carried out on single n-alkanes, so it is likely that inhibitor associations are specific to certain homologues. In the case of the Inhibitor 1 family, the closer the length of the inhibitor chain was to the shorter and more soluble n-alkane chain lengths, the less effect it appeared to have. This may reflect a closer interaction of the interacting species in the solution environment. This would decrease the effective concentration of additive



Figure 6. The turbidity plot for wax and inhibitor 1 (16) mediated wax solution cooled at 0.1 °C/min, showing Tcryst and Tdiss.

Figure 7. The turbidity plot for wax and inhibitor 1 (22) mediated wax solution cooled at 0.1 °C/min, showing Tcryst and Tdiss.

with respect to the remaining homologues, and the overall crystallization temperature would be affected to a lesser extent. Double hysteresis curves found in the case of Inhibitor 1 (20) and Inhibitor 1 (22) indicated that crystallization of some components within the homologous fraction occurred early on, followed by the rest at a later stage. The step changes in transmittance in the turbidity profile for Inhibitor 2 (20-24) mediated wax is of particular interest as this inhibitor contains alkyl chain lengths of 20 and 22 carbons, like Inhibitor 1 (20) and Inhibitor 1 (22), which caused double hystereses in the other family of inhibitors. This indicates that a close match with the lowest homologues in the wax mixture could cause the step changes observed. The inhibitor retained some activity, however, because the overall crystallization temperatures were lower than for the pure wax, and the saturation temperatures invariably increased, indicating changes in Gibb’s free energy of dissolution with additive addition.

Analysis of wax crystallized in the presence of additive inhibitor 2 (24-28), which possesses alkyl chains containing 24-28 carbons, revealed a reduction in crystallization temperature and the greatest increase in saturation temperature with respect to the additive free sample. The inhibitor chain length blend was of the same order as the carbon chain lengths of the n-alkanes present in the highest proportions in the homologous wax mixture. The fractional crystallization effects observed in the present work, which have also been reported in the literature by Chichakli et al.,6 would be consistent with the inhibitor cocrystallizing with the lower homologue fractions, hence acting as a nucleator. Industrially, such behavior would be undesirable, as the concentration and hence activity of the inhibitor would be bound to decrease with the cocrystallization process. A further and undesired ramification of such action would be that the inhibitor/lower n-alkane complex could provide secondary nuclei, hence promoting the crystallization of the remaining homologous fractions.


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Figure 8. The turbidity plot for wax and inhibitor 2 (20-24) mediated wax solution cooled at 0.1 °C/min, showing Tcryst and Tdiss.

Figure 9. The effect of inhibitor alkyl chain length on crystallization temperature and MSZW. The inhibitor family is represented by I1 and I2, with the chain length in parentheses.

The observed decrease in the crystallization temperatures for the additive-mediated systems when compared to measurements made in their absence are consistent with the decreases in crystallization temperature reported elsewhere,3-5,21-23 which were largely ascribed to inhibitor/wax interactions in solution. The increase in saturation temperature observed implies a decrease in solubility of the additive-mediated crystals, perhaps reflecting the lower entropy of dissolution for the additive-mediated wax crystal. The presence of polymeric additive in the crystal would be expected to

increase the disorder as its bulky groups would distort the intermolecular packing in the wax crystals. This supposition is consistent with the reduction of ∆S observed by Ding et al7 for polymer-mediated waxes, reflecting the fact that a lower ∆S would result in a less negative free energy of dissolution. In other words, dissolution of the additive-mediated crystal would be less energetically favorable. 4.2. Analysis of the SAXS/WAXS Data. The average carbon chain length of model wax is 27 carbons. The computer program Dragon16 was used to obtain all of



Figure 10. Powder diffraction pattern of model wax taken using a Siemens D500 diffractometer. Table 1. Comparison between the Crystallization, Dissolution Temperatures, and MSZW for Model Oil in the Absence and Presence of Each of the Inhibitors sample

crystallization temp

MSZW

model oil model oil + 400 ppm Inhibitor 1 (16) model oil + 400 ppm Inhibitor 1 (18) model oil + 400 ppm Inhibitor 1 (20) model oil + 400 ppm Inhibitor 1 (22) model oil + 400 ppm Inhibitor 2 (16) model oil + 400 ppm Inhibitor 2 (20-24) model oil + 400 ppm Inhibitor 2 (24-28) model oil + 400 ppm Inhibitor 2 (>30)

18.9 16.9 17.7 19.1 19.4 16.1 16.0 16.0 17.9

1.6 4.0 5.7 5.7, 9.8 4.1,10.6 5.5 8.1 10.2 5.8

the reflections for C27H56. C27H56 is known to crystallize in the space group Pbcm, and its published unit cell parameters were used in Dragon to approximate the peak positions for model wax. The peaks at 4.48, 6.74, and 10.04° 2θ are clearly the c-axis peaks (004), (006), and (008) respectively. The prominent peak at 21.2° 2θ could be 110, 110, or 112, and the peak at 23.58° 2θ could be 021 or 020. Comparison with the literature data suggests that these peaks would be consistent with the 110 and 020 peaks, respectively. Since this is a multihomologous wax, it is difficult to index with confidence the higher hk0 reflections without a detailed molecular structure; however, higher reflections were not seen in the SAXS/WAXS plots, so it is not necessary to qualify the indexation of the 2 theta values. Correlating the length of the c-axis with average carbon number as seen in Figure 1, a c-axis of 78.8 Å for the ex-situ XRD analysis of the wax indicates an average carbon number of 28 carbons. The ratio of b/a for the ex-situ wax powder was 1.5, indicating orthorhombic symmetry as expected. Examination of the waxes crystallized in the in-situ WAXS/SAXS experiments revealed a considerably longer c-axis for the unit cell than that found for the model wax as measured ex-situ. The ratio of b/a however remained constant at 1.5, indicating that orthorhombic symmetry was broadly maintained, with no evidence for the formation of a rotator phase. Comparison of the measured c-axis to the chart provided in Figure 1 reveals the average carbon chain length to be about 31

carbons, i.e., close to the maximum carbon chain length present within the homologous mixture. Higher molecular weight n-alkanes are less soluble than the lower homologues, and the longer c-axis length of the solution crystallized wax prepared in-situ would suggest that the heavier n-alkanes crystallized first. The length of the c-axis was not found to vary throughout the cooling/heating cycle. This is different from the data obtained by Chevalier et al.14 in which the length of the c-axis decreased on cooling. However, they were studying a different wax/solvent system, and cooled the solution at 1 °C/min compared with 0.5 °C/min for the experiments presented in this paper. They found that the initial c-axis length corresponded to a chain length slightly lower than the maximum chain length in their wax mixture, which is consistent with the results obtained here. All of this suggests the formation of a lower density wax crystal with void formation, as opposed to the chain folding mechanisms observed in crystallization from the melt. The size of the wax crystal lattice clearly increased on addition of inhibitor in the case of Inhibitor 1 (22) and Inhibitor 2 (16). It is difficult to discuss changes in the data taken using Inhibitor 1 (16) as the 020 peak was not detected in that case. While this could indicate disruption in the interlamellar molecular packing, it could also equally simply reflect texture effects in the crystal/solution slurry. The central position of the amorphous halo, which provides a measure of the intermolecular aggregation and clustering in solution,


Hennessy et al.

Figure 11. A 3-D stackplot of (a) the WAXS and (b) the SAXS data obtained during the crystallization of and 800 ppm Inhibitor 1 (22) in 10% model oil solution during a cooling and heating cycle. Table 2. Calculated Lattice Parameters for Each of the Samples under Study, with Position of the Amorphous Halo, and Published Lattice Parameters for Three n-Alkanes sample

a/Å

b/Å

c/Å

ex-situ powder wax 10% model oil 800 ppm Inhibitor 1 (16) 800 ppm Inhibitor 1 (22) 800 ppm Inhibitor 2 (16) C29H60 C31H64 C33H68

5.04

7.54

78.8

4.88

7.32

88.6 88.6

5.16

7.72

88.6

4.94

7.42

4.95 4.93 5.00

7.44 7.44 7.46

volume Å3

b/a

2995

1.5 1.5 unknown

4.52 4.48

3529

1.5

4.69

88.6

3248

1.5

4.58

77.5 82.6 87.67

2854 3030 3270

1.5 1.5 1.5

indicated increases in d spacing in the same order as the additive-mediated wax crystal lattice increases, supporting a model in which the inhibitor and paraffin species associate in solution as a precursor to crystallization. The backbone of the Inhibitor 1 (22) polymer may be thought of as planar, with a C-C bond distance of 1.28 Å (Figure 12). This gives an overall distance between chains of 5.12 Å. With a calculated a-axis value of 5.16

3165 unknown

position of halo/Å

Å for the Inhibitor 1 (22) mediated wax, it is likely that lattice matching occurred for this sample. While the size of the a-axis increased, the b-axis also increased to maintain the ratio of 1.5 for b/a. Orthorhombic symmetry was maintained in the additive-mediated wax crystals. In the case of Inhibitor 2 (16), alkyl chains are thought to protrude from alternating sides of the polymer backbone. The C-C bond distance along the longitudi-


Figure 12. Conformation of the Inhibitor 1 (22) molecule in zigzag confrmation.

Figure 13. Conformation of the Inhibitor 2 (16) molecule in zigzag confrmation.

nal axis is 1.28 Å, and the C-N bond distance is 1.47 Å. This yields an overall distance of 7.44 Å between adjacent alkyl chains as illustrated in Figure 13. With a calculated b-axis value of 7.42 Å for Inhibitor 2 (16), it is likely that lattice matching took place. Orthorhombic symmetry was maintained in these additive-mediated wax crystals. The length of the c-axis was unaffected by the presence of additive. This indicated that the length of the alkyl chain of the additive did not influence the unit cell volume of the crystallizing wax at these concentrations. Inhibitor 1 (16) is of the same family of inhibitors as Inhibitor 1 (22), yet the 110 reflection was clearly not in the same position as that observed for the Inhibitor 1 (22) mediated wax crystallization. This could contradict the idea that b-axis lattice matching is taking place for the inhibitors. The actual 2θ value is so close to that for the wax that it is probable that very few inhibitor/ wax interactions are occurring. 4.3. General Discussion. While previous research7,26,27 has suggested epitaxial crystallization between additives and wax, this work, to our knowledge, is the first to give experimental evidence of lattice matching between the alkyl chains of the host wax and the mediating alkylated additive. It would be expected that toluene in the solution would keep the polar backbone of the inhibitor dissolved,22 and the alkyl chains would interact with the waxes to varying degrees, depending on their chain length. In this way, it could be postulated that the inhibitors would keep the waxes in solution for longer during the cooling process, as they increase the crystal-solution interfacial tension, and eventually cocrystallize with the waxes. The resulting crystals were found to have larger unit cell volumes, consistent with lower lattice energies and lower enthalpies of crystallization, as reported in the literature. The higher saturation temperatures measured for the additive-mediated samples probably reflect the disrupting effect of the inhibitors leading to greater disorder than


Figure 14. A schematic illustrating a possible inhibitor mechanism. The thick dotted line represents the inhibitor backbone. The thick black lines are the inhibitor alkyl chains, the waves are toluene molecules, and the faint dotted lines represent wax molecules possessing orthorhombic symmetry.

a pure wax crystal. This means the change in entropy between the dissolved and crystalline state is less, leading to a more positive free energy change for the additive-mediated wax, which means dissolution is less likely for the additive-mediated crystals. A schematic diagram illustrating a tentative model for the additive/wax interaction is shown in Figure 14, revealing the interaction of the inhibitor molecules with the wax, allowing it to maintain orthorhombic symmetry, while influencing the short axes of the forming crystal. From these results, the following model is proposed to rationalize the observed experimental data. Decreased crystallization temperatures in the turbidity rig, and the position of the amorphous halo in the X-ray diffraction data suggested inhibitor/wax ordering in solution prior to crystallization, with increased inhibitor/ wax interactions lowering the respective wax/wax interactions. From this work, it seems pertinent to suggest that the family of inhibitor used affects the a or b axes of the wax, and positive epitaxial relationships have been observed. The decreases in enthalpy of crystallization observed by other workers are supported by the increases in unit cell volume and corresponding decreases in lattice energy. The c-axis of the wax is determined by the longest chain length of the crystallizing wax mixture. The cocrystallization of additive and wax is consistent with a large entropy increase in the additive-mediated crystal compared to the pure wax. Other workers observed an entropy increase for additive-mediated waxes. This explains the large increases in dissolution temperatures, as the free energy of dissolution would therefore be less negative for additivemediated waxes. Finally, the activity of the inhibitor is determined by its alkyl tail length, and the chain length distribution of the wax mixture. Too close a match between the inhibitor and the wax would decrease the inhibitor’s effectiveness, as interactions are centered too specifically on one homologue. The increase in crystallization temperature as the inhibitor chain length approached 22 carbons supports this idea. 5. Conclusions The presence of flow-improving inhibitor in the wax solution invariably caused a decrease in crystallization temperature and an increase in dissolution temperature of the wax. This is indicative of inhibitor wax ordering in solution prior to crystallization, with increased inhibitor wax interactions lowering the respective wax/ wax interactions. The cocrystallization of additive and wax is consistent with a large entropy increase in the


additive-mediated crystal compared to the pure wax. Other workers observed an entropy increase for additive-mediated waxes. This explains the large increases in dissolution temperatures, as the free energy of dissolution would therefore be less negative for additivemediated waxes. The double hystereses observed in the turbidity curves for some of the additive-mediated solutions suggest fractional crystallization, where some homologues in the wax mixture crystallized before the others. Positive epitaxial relationships were observed between the additive-mediated wax and the polymer chains. The activity of the inhibitor is determined by its alkyl tail length, and the chain length distribution of the wax mixture. Too close a match between the inhibitor and the wax would decrease the inhibitor’s effectiveness, as interactions are centered too specifically on one homologue. Acknowledgment. We gratefully acknowledge Heriot-Watt University for the award of a Ph.D. research studentship20; BP Exploration in Sunbury UK for stimulating this research topic and for additional support of this research; Marion Millar for her help with the GC analysis; and Ernie Komanschec at CCLRC Daresbury Laboratory for help with the synchrotron SAXS/WAXS experiments on station 8.1 at the SRS. References (1) Jorda, R. M. JPT 1966, 1605. (2) Craig, S. R.; Hastie, G. P.; Gerson, A. R.; Roberts, K. J.; Sherwood, J. N.; Tack, R. D. J. Mater. Chem. 1997, 8, 859. (3) Beaney, D.; Mullin, J. W.; Lewtas, K. J. Cryst. Growth 1990, 102, 801. (4) Ruehrwein, R. Proc. Third World Pet. Congr. 1951,V11, 423. (5) Bormann, K.; Rodig, J. Chem. Technol. 1975, 27, 743. (6) Chichakli, M.; Jessen, F. W. Ind. Eng. Chem. 1967, 59, 86. (7) Ding, X.; Qi, G.; Yang, S. Polymer 1999, 40, 4139.

Hennessy et al. (8) Chevallier, V.; Petitjean, D.; Ruffier-Meray, V.; Dirand, M. Polymer 1999, 40, 5953. (9) Craig, S.; Hastie, G.; Roberts, K. J.; Sherwood, J. N. J. Mater. Chem. 1994, 4, 977, (10) Hastie, J. P.; Roberts, K. J. J. Mater. Sci. 1994, 29, 1915. (11) Dirand, M.; Chevallier, V.; Provost, E.; Bouroukba, M.; Petitjean, D. Fuel 1998, 77, 1253. (12) Dorset, D. Acta Crystallogr., Sect. B: Struct. Sci. 1995, B 51, 1021. (13) Gerson, A. R.; Nyburg, S. C.; McAleer, A. J. Appl. Crystrallogr. 1999, 32, 296. (14) Chevallier, V.; Bouroukba, M.; Petitjean, D.; Dirand, M.; Pauly, J.; Daridon, J.; Ruffier-Meray, V. Fuel 2000, 79, 1743. (15) Luth, H.; Nyberg, S. C.; Robinson, P. M.; Scott, H. G. Mol. Cryst. Liq. Cryst. 1972, 27, 337. (16) Cockcroft, J. K. Inst. Laue Langevine 1968. (17) Gerson, A. R.; Roberts, K. J.; Sherwood, J. N. Powder Technol. 1991, 65, 243. (18) Rossi, A. An Examination of the Inter-Relationship Between Structure and Kinetics Associated with Crystallisation of Single and Mixed Chocolate Confectionary Fats. Ph.D. Thesis, Strathclyde University, 1998. (19) MacCalman, M. L. Studies of the Crystallisation of some Pharmaceutically Important Materials in Relation to Polymorphic Structural Stability. Ph.D. Thesis, Strathclyde University, 1996. (20) Hennessy, A. J. B. An Examination of Additive Mediated Wax Crystallisation in Oil-Pipeline Environments. Ph.D. Thesis, 2001. (21) Holder, G. A.; Thorne, J. ACS Div. Polym. Chem. 1979, 20, 766. (22) Heraud, A.; Pouligny, B. J. Colloid Interface Sci. 1992, 153, 2, 378. (23) Hennessy, A. J.; Neville, A.; Roberts, K. J. J. Cryst. Growth 1999, 199, 830. (24) Denicolo, I.; Craievich, A. F.; Doucet. J. J. Chem. Phys. 1984, 80, 6200. (25) Dirand, M.; Chevallier, V.; Provost, E.; Bouroukba, M.; Petitjean, D. Fuel 1998, 77, 1253. (26) Giorgio, S.; Kern, R. J. Cryst. Growth 1983, 62, 360. (27) Kern, R.; Dassonville, R. J. Cryst. Growth 1992, 116, 19.

CG0341050

WAXS and Turbidity Studies of the Structure and

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