Effect of Cooling Rate on Crystallization of Model Waxy Oils with

The development of offshore oil production, especially in deeper water,1,2 means .... of paraffins were calculated from the peak areas using the Pyris...
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Energy & Fuels 2006, 20, 250-256

Effect of Cooling Rate on Crystallization of Model Waxy Oils with Microcrystalline Poly(ethylene butene) Xuhong Guo,† Brian A. Pethica,† John S. Huang,† Douglas H. Adamson,‡ and Robert K. Prud’homme*,† Department of Chemical Engineering and Princeton Materials Institute, Princeton UniVersity, Princeton, New Jersey 08544 ReceiVed May 31, 2005. ReVised Manuscript ReceiVed August 12, 2005

The crystallization of long-chain n-paraffins and their binary mixtures from model waxy oils with decane as the solvent has been studied as a function of cooling rates by rheology, optical microscopy, and differential scanning calorimetry (DSC). The yield stresses of the gels formed upon cooling solutions of n-hexatriacontane (C36) and n-dotriacontane (C32) in decane increase with faster cooling rate, while for n-octacosane (C28) they decrease. DSC shows that the pure C28 wax precipitated from solution comprises multiple metastable phases as has been shown previously by X-ray scattering. Crystallization of C36 + C32 mixtures gives solid solutions with the yield stresses increasing with cooling rate, similar to the behavior of the pure component waxes. C36 and C28 crystallize separately from their mixed solution as observed by DSC. Addition of microcrystalline poly(ethylene butene) (PEB) wax crystal modifiers to single or mixed solutions greatly reduces the gel yield stress. The PEBs reduce crystal sizes and change morphologies significantly. DSC thermograms on the separated crystals show that the co-crystallization of PEB with C28 creates additional trapped metastable solid phases that appear between 51 and 73 °C. The magnitude and breadth of the peaks depend on the cooling rate as would be expected for the kinetic trapping of metastable phases.

Introduction Paraffin wax precipitation and deposition can lead to blockages of pipelines during transport of crude oil. The development of offshore oil production, especially in deeper water,1,2 means that the economic consequences of pipeline blockage and the cost of repeated mechanical removal of wax by pigging3 are becoming more severe. Wax deposition depends on several factors, notably wax content and composition, flow rate, the temperature difference between oil and pipe surface, and the cooling rate along the pipeline.4 Recent work by Singh and Fogler5 has validated a dynamic model of wax deposition that includes these variables. However, the model does not address the yield stresses of the wax layer that is deposited, which will influence the frequency with which mechanical removal must be performed. In our previous work, we presented the results on the rheology and yield stresses of model long-chain paraffin gels.6,7 The reduction or elimination of yield stress was achieved by the addition of microcrystalline polymers: one based on polyethylenepoly(ethylenepropylene) (PE-b-PEP) self-assembling block co* To whom correspondence should be addressed. E-mail: [email protected]. † Department of Chemical Engineering. ‡ Princeton Materials Institute. (1) Singh, P.; Venkatesan, R.; Fogler, H. S.; Nagarajan, N. R. AIChE J. 2001, 47, 6. (2) Ribeiro, F. S.; Souza, P. R.; Mendes, S.; Braga, S. L. Int. J. Heat Mass Transfer 1997, 40, 4319. (3) Denis, J.; Durand, J. P. ReV. Inst. Fr. Pet. 1991, 46, 637. (4) Misra, S.; Baruah, S.; Singh, K. SPE Prod. Facil. 1995, 10, 50. (5) Singh, P.; Fogler, H. S.; Nagarajan, N. J. Rheol. 1999, 43, 1437. (6) Ashbaugh, H. S.; Fetters, L. J.; Adamson, D. H.; Prud’homme, R. K. J. Rheol. 2002, 46, 763. (7) Ashbaugh, H. S.; Radulescu, A.; Prud’homme, R. K.; Schwahn, D.; Richter, D.; Fetters, L. J. Macromolecules 2002, 53, 7044.

polymers,6 the other based on microstructured crystallizable poly(ethylene butene) (PEB).7 In those studies, we considered wax alkane number, polymer concentration, and polymer architecture. However, the effect of cooling rate was not fully explored. It is known that the cooling rate can affect the morphology of paraffin crystals,4,8-11 the transition temperature, and the yield stress of gels formed from waxy oils.5,12,13 However, investigation of the influence of cooling rate on the behavior of waxy oils is incomplete, especially with polymer additives. Webber et al.11 found that two kinds of mineral oil, Exxon (EX) and Chevron RLOP (CH), showed different dependencies of the gel properties on cooling rate. The yield stresses increased weakly with increasing cooling rate for CH but were almost independent of the cooling rate for EX. Webber also reported that an increase in the cooling rate caused the crystallization onset temperature to decrease for both EX and CH.11 Moreover, he noted that the crystal size decreased with increasing cooling rate, which is consistent with the observation of other authors.4,10 Singh et al. observed a significant depression in the gel point with decreasing cooling rate of a model waxy oil consisting of a food grade wax (Mobil M140) and a 3:1 mixture of mineral oil (Blandol) and kerosene as solvent.5 Holder and Winkler indicated that the shape of wax crystals was changed from single (8) Holder, G. A.; Winkler, J. Nature 1965, 207, 719. (9) Halter, E.; Kanel, J.; Schruben, D. In Fundamental Aspects of Crystallization and Precipitation Processes; Briedis, D. M., Ramanarayanan, K. A., Eds.; AIChE Symp. Ser. 253; American Institute of Chemical Engineers: New York, 1987; p 31. (10) Anderson, T.; Peters, H. S.; Torres, R. A.; Nagy, N. A.; Schruben, K. L. Fuel 2001, 80, 1635. (11) Webber, R. M. J. Rheol. 1999, 43, 911. (12) Gimzewski, E.; Audley G. Thermochim. Acta 1993, 214, 149. (13) Hammami, A.; Mehrotra, A. K. Fuel 1995, 74, 96.

10.1021/ef050163e CCC: $33.50 © 2006 American Chemical Society Published on Web 11/25/2005

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dendrites to twin dendrites when light, catalytically cracked oil was cooled at a rate of 2 °F/h instead of 1 °F/h.8 The aim of this study is to demonstrate the effect of cooling rate on the yield stress of the gels formed from model waxy oils prepared by dissolving long-chain n-paraffins C36, C32, and C28 individually and in their binary mixtures in decane. Crystallization from both melts and from decane solutions is studied by DSC, and the morphology of these paraffin crystals are observed by optical microscopy. We also investigate the effect of cooling rate on paraffin crystallization when PEB wax modifiers are added to the decane solutions. Experimental Section Materials. Decane (anhydrous, 99+%), octacosane (C28, >99%, F.W. 394.77, mp 59 °C), dotriacontane (C32, >97%, F.W. 450.88, mp 69 °C), and hexatriacontane (C36, >98%, F.W. 506.99, mp 74-76 °C) were purchased from Aldrich and were used as obtained. Analysis by gas chromatography (GC) gave for the C36 sample a composition of 97.6% C36, 2.1% C34, and 0.2% C38. For the C32 sample it gave 98.8% C32, 0.4% C31 and C34, and 0.8% other paraffin isomers. The C28 sample gave a purity of 99.6%, with 0.38% each of C26 and C30. No fatty acids or alkanols could be observed in the samples by IR analysis. Model waxy oil samples were prepared by dissolving C28, C32, C36, or their binary mixtures in decane and heating at 20 °C/min to 70 °C, above the melting temperature of the waxes. The samples were held at temperature for 5 min. Solid crystal samples were prepared by cooling the model waxy oils from 70 to 0 °C at a cooling rate of 1, 5, or 10 °C/min and separating the precipitated crystals by filtration with vacuum in an ice bath and drying under vacuum at room temperature for 3 days. Crystal samples were sealed and stored at ca. -4 °C before using. The synthesis of the microcrystalline random copolymers PEB is described elsewhere.7 The final polymers had molecular weights of ca. 7000 g/mol and a distribution of molecular weight of ca. 1.03. Two PEBs (PEB7.5 and PEB10) were used (the number denotes the ethyl side branches per 100 backbone carbons as determined via H1 NMR). Yield Stress Measurement. The yield stress (τy) is defined as the stress below which no flow occurs. An operational definition of τy was adopted as the stress at the transition between the creep and liquid-like viscosity regimes where τy can be identified as the stress for which the derivative is a maximum.9 The yield stress measurements were performed on a Rheometrics DSR controlled stress rheometer with a 40-mm plastic parallel plate. The temperature was controlled to within 0.1 °C by a Peltier plate. To minimize evaporation, the sample was covered with a solvent trap. The samples were initially heated to 70 °C at a rate of ca. 20 °C/min, kept at this temperature for 5 min to erase their thermal history, and then cooled to the experimental test temperature of 0 °C at 1, 5, or 10 °C/min. After allowing the sample to anneal at constant temperature under no stress for 20 min in the case of 10 °C/min (15 min for 5 °C/min and 0 min for 1 °C/min), we applied a static stress and incrementally increased it every 10 s (100 stress increments per decade) and measured the viscosity. As discussed below, the annealing time has no effect on the measured yield stress at any cooling rate. The initial applied stress was chosen well below the stress at which creep begins. Optical Microscopy. Wax crystal morphologies were observed using a Nikon TE200 inverted microscope with phase and DIC optics (Micron Optics, Cedar Knoll, NJ). Images were captured using a Kodak ES 310 CCD camera connected to a PC via a PIXCID imaging board (EPIX, Buffalo Grove, IL). A small quantity of wax crystals was transferred from storage at -4 °C directly to a glass slide inside a copper stage with a central window for observation. The temperature of the copper stage was controlled at 0 °C by a circulating bath. Images were taken at five sites on the slides.

Figure 1. Dependence of yield stress for model waxy oils on cooling rate. The solutions were heated to 70 °C and cooled to 0 °C at various cooling rates. Yield stresses were measured at 0 °C. Error bars are the standard deviations from four measurements for each sample. (O) 4%C36; (0) 4%C32; (3) 4%C28; (b) 2%C36 + 2%C32; and (9) 2%C36 + 2%C28.

Figure 2. Comparison of the cooling rate effects on the yield stresses of gels from decane solutions of 4%C28, 4%C28 + PEB10, and 4%C28 + PEB7.5. (O) 4%C28; (3) 4%C28 + 0.1%PEB7.5; (4) 4%C28 + 0.8%PEB7.5; (0) 4%C28 + 0.8%PEB10; and (×) 4%C28 + 0.1%PEB10. Measurement temperature is 0 °C.

Differential Scanning Calorimetry (DSC). The differential scanning calorimeter is a Perkin-Elmer (Norwalk, CT) Pyris DSC 7. The temperature scale was calibrated by the melting temperature of ice from DI water and the heat flow by the fusion of an indium standard. An empty stainless steel sample pan was used as the reference, and the baseline was established by running an empty pan before the sample measurement. About 10 mg of solid paraffin or model waxy oil was weighed into a pan and hermetically sealed. The pan was then placed into the DSC sample tray. Scanning rates ranged from 1 to 10 °C/min, and the temperature ranges were chosen to ensure that all peaks appeared and the baseline was stable for at least 10° before the first peak and after the last peak. The sample chamber was continuously purged with dry nitrogen. The enthalpies of crystallization and melting of paraffins were calculated from the peak areas using the Pyris software. Regular sampling showed no weight loss from the hermetically sealed sample pans.

Results and Discussion Yield Stress. For the model waxy oils composed of single long-chain n-paraffins in decane, the dependence of the gel yield stress on cooling rate varies with the paraffin (Figure 1). The measurements were repeated at least four times, and the error bars show the standard deviation of the values. Although for some points the variability is large, the trends are that the gel yield stress increases with cooling rate for C36 and C32 but decreases for C28. At this time we do not have a definitive

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Figure 3. Yield stresses of model waxy oils 4%C36 and 4%C32 as a function of cooling rate. (a) 4%C32. (O) 4%C32; (0) 4%C32 + 0.1%PEB10; and (3) 4%C32 + 0.1%PEB7.5. (b) 4%C36. (O) 4%C36; (0) 4%C36 + 0.1%PEB10; and (3) 4%C36 + 0.1%PEB7.5. Measurement temperature is 0 °C.

Figure 4. Yield stresses of gels from model waxy oils 2%C36 + 2%C32 and 2%C36 + 2%C28 as functions of solution cooling rate under the effect of PEB. (a) 2%C36 + 2%C32. (O) Without PEB; (0) with 0.1%PEB10; (3) with 0.1%PEB7.5; (×) with 0.05%PEB10 + 0.05%PEB7.5. (b) 2%C36 + 2%C28. (O) without PEB; (0) with 0.1%PEB10; (3) with 0.1%PEB7.5; (×) with 0.05%PEB10 + 0.05%PEB7.5. Measurement temperature is 0 °C.

explanation for the origin of the apparently anomalous behavior of the C28 wax. However, we believe it is related to the various metastable rotator phases that C28 is known to form.14-16 The DSC results, to be discussed later in the article, also show this multiphase behavior. Therefore, cooling rate might be expected to change the relative volume fractions of the metastable phases, and this is seen in the changes in the DSC traces with varying cooling rates. The reduction of yield stress could be thought of as a dilution effect: mixing two immiscible wax phases causes a reduction in the yield stress relative to the value of either pure component at the same solids level.17 Figure 1 also displays the yield stress of the gels from model waxy oils composed of binary mixtures of paraffin C36 + C32 and C36 + C28 as a function of the cooling rate. We previously showed that wax mixtures with carbon numbers varying by more than 4 form separate crystal phases.17 Therefore, the reduction (14) Sirota, E. B.; Singer, D. M. J. Chem. Phys. 1994, 101, 10873. (15) Sirota, E. B.; King, H. E.; Singer, D. M.; Shao, H. H. J. Chem. Phys. 1993, 98, 5809. (16) Dirand, M.; Bouroukba, M.; Chevallier, V.; Petitjean, D. J. Chem. Eng. Data 2002, 47, 115.

of the yield stress for the mixture can be thought of as a dilution of the volume fraction of the wax phase relative to the percolation threshold.17 The yield stresses of the mixtures increase with cooling rate, which would be consistent with less phase demixing. Changing the annealing time after formation of the gels from 0 min to 2 h has no effect on the measured yield stress. As shown in Figure 2, when wax modifier PEB10 or PEB7.5 is added to 4%C28 solutions, the gel yield stress decreases sharply. With PEB10 more effective than PEB7.5, PEB10 reduces the yield stress from more than 200 Pa on cooling at 1 °C/min to ∼1 Pa. We have previously shown by neutron scattering that the effectiveness of PEB7.5 is related to its crystallization temperature in solution.7 The maximum reduction in yield stress occurs for polymers that co-crystallize at the same temperature as the wax phase. The yield stress is not very dependent on the concentration of PEB10 from 0.1 to 0.8% with the solution cooling rate shown. The gel yield stress in the (17) Guo, X.; Pethica, B. A.; Huang, J. S.; Prud’homme, R. K.; Adamson, D. H.; Fetters, L. J. Energy Fuels 2004, 18, 930.

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Figure 5. Comparison of optical micrographs of solid crystal samples from 4%C36 with and without PEB at various cooling rate. (a1) Crystals separated from 4%C36 solution cooled from 70 to 0 °C at 1 °C/min; (a2) 4%C36 at 5 °C/min; (a3) 4%C36 at 10 °C/min; (b1) 4%C36 + 0.1%PEB10 at 1 °C/min; (b2) 4%C36 + 0.1%PEB10 at 5 °C/min; (b3) 4%C36 + 0.1%PEB10 at 10 °C/min; (c1) 4%C36 + 0.1%PEB7.5 at 1 °C/min; (c2) 4%C36 + 0.1%PEB7.5 at 5 °C/min; (c3) 4%C36 + 0.1%PEB7.5 at 10 °C/min. Black bars represent 10 µm.

presence of PEB is not significantly affected by increasing solution cooling rate. The same pattern as that for C28 is seen in the yield stresses of the gels from solutions of C32 and C36 with or without added PEBs (Figure 3, parts a and b). On addition of the polymers, the yield stresses are reduced by more than 2 orders of magnitude, as shown in Figure 3, with insignificant effect from changing the cooling rates. Figure 4a shows the effect of cooling rate on the yield stresses of gels formed from decane solutions of 2%C36 + 2%C32 without added wax inhibitor, and in the presence of PEB10 and PEB7.5 separately or together. The greatest reduction in the yield stress of the mixed paraffins is given by PEB7.5. The PEBs are less effective at reducing the yield stresses of gels of the C36 + C32 mixtures (Figure 4a) than of the pure paraffin gels (Figure 3). Given the experimental error of (2 Pa for the yield stress measurement, there is no discernible effect of cooling rate on the wax gels with PEB (except for the relatively ineffective PEB10, which has the same trend with cooling rate as the C36 + C32 wax; Figure 4a). Morphology. The morphology of long-chain n-paraffin crystals formed from decane solution was observed using optical microscopy. The micrographs in Figure 5 show that the size and appearance of C36 crystals from decane solution are not dramatically altered by cooling rate. While the addition of PEB changes crystal size and morphology (Figure 5, parts a1, b1, and c1; i.e., looking down a column of figures), cooling rate changes neither size nor morphology appreciably (Figure 5, parts b1, b2, and b3; i.e., looking across a column of figures). This is consistent with the lack of dramatic change in yield stress values with cooling rate, but the large change in yield stress with PEB addition. The morphologies of crystals of all three paraffins at 0 °C, not separated from decane, are shown in a previous publication.17

Figure 6. Solubility of C32 in decane determined by different methods. (O) By DSC with scan rate 10 °C/min; (0) by DSC with scan rate 5 °C/min; (3) by DSC with scan rate 1 °C/min; (b) by rheology; and (9) visually observed.

Onset of Precipitation. Several methods were used to determine the onset temperature of paraffin crystallization in this work. DSC was performed at three scan rates of 10, 5, and 1 °C/min, while the rheological determination of gel point was conducted at a cooling rate of 0.5 °C/min, and the visual observation of the crystallization temperature was performed by checking the samples 30 min after decreasing the temperature in 1 °C increments corresponding to a cooling rate of 0.033 °C/min.6 Figure 6 shows the onset temperature of precipitation determined by three methods for C32 at various concentrations in decane. The “apparent solubility” boundary moves toward lower temperature with increasing cooling rate. The shift of solubility boundary to lower temperature with increasing cooling rate was also observed in the case of C36 (Figure 7a), C28 (Figure 7b), and for waxes with added PEBs (Figure 8). This phenomenon

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Figure 7. Solubility as function of temperature for (a) C36 and (b) C28 in decane determined by DSC. (O) Scan rate 10 °C/min; (0) scan rate 5 °C/min; and (3) scan rate 1 °C/min.

Figure 8. Effect of PEBs on solubility boundaries of C36 determined by DSC. (a) C36 + 0.05%PEB10 and (b) C36 + 0.05%PEB7.5. (O) At the scan rate of 10 °C/min; (0) 5 °C/min; and (3) 1 °C/min.

is expected due to a combination of kinetic effects for nucleation and growth of the crystals and thermal lag in heat transfer. An analysis of the data to determine apparent enthalpies and entropies would involve plotting 1/T versus the ln(mole fraction of wax).6,18 For this discussion, plotting solubilities and temperatures gives a more direct representation of the effect of cooling rate on precipitation. The addition of PEB does not significantly alter the appearance temperature at any cooling rate for either the single or mixed long-chain paraffins in decane (compare Figures 7a and 8a for C36; results were similar for C32, C28, and the mixed wax systems). Thus, PEB is not an inhibitor of nucleation, nor is it a nucleating agent. This is consistent with our previous observation by small-angle neutron scattering that PEB7.5 and PEB11 co-assemble with wax structures in decane solutions upon cooling.7 Crystals from Solution. The phases comprising the wax crystals that precipitated from solution were probed by DSC. Wax crystals that precipitated from decane solutions were isolated by cooling the solutions from 70 to 0 °C at cooling rates of 10, 5, or 1 °C/min. The crystals were filtered, and the remaining decane was removed in vacuo. The crystals were scanned by DSC from 25 to 90 °C at 1 °C/min. After the first

DSC scan, the melted wax was recrystallized in the DSC pan by cooling from 90 to 25 °C at 1 °C/min. These samples are designated as “second heating” samples in Figures 9 and 10. The recrystallized samples were again scanned to 90 °C at 1 °C/min. Figure 9 displays the DSC traces of crystals from 4%C36 with and without PEB. The dotted curve represents the properties of crystals formed from the melt during the second heating. Two separate peaks appear in the DSC trace during the second heating, and the peak at lower temperature denotes the solidsolid transition from monoclinic structure to RIII rotator phase for C36 while the other peak represents the phase transition from RIII to melt18,19 (see Figure 4 of Sirota et al. for the complete phase diagram of the pure wax systems). For the crystals precipitated from solution, the low-temperature peak associated with the monoclinic phase is suppressed. This is consistent with the greater degree of mobility for crystals formed from solution. The solid-solid transition peak merges into the main melting peak at ∼75 °C, which is consistent with (18) Guo, X.; Pethica, B. A.; Huang, J. S.; Prud’homme, R. K. Macromolecules 2004, 37, 5638. (19) Sirota, E. B.; King, H. E.; Shao, H. H.; Singer, D. M. J. Phys. Chem. 1995, 99, 798.

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phase structure of C28 is dramatically more complex than that of C36 (or C32; data not shown, but it is qualitatively similar to the C36 data). Clearly additional research is warranted, using other microprobes of structure, to fully characterize the C28 wax phase behavior. Conclusions

Figure 9. DSC thermographs for solid crystal samples from (a) 4%C36, (b) 4%C36 + 0.1%PEB10, and (c) 4%C36 + 0.1%PEB7.5 with various cooling rate. The top dotted curve is the second heating of a crystal sample prepared at a cooling rate of 10 °C/min; the solid curves from top to bottom denote the first heating of samples prepared at cooling rates of 10, 5, and 1 °C/min, respectively.

Figure 10. DSC thermographs of solid crystal samples from (a) 4%C28, (b) 4%C28 + 0.1%PEB10, and (c) 4%C28 + 0.1%PEB7.5 with various cooling rates. Solid curves from top to bottom represent the first heating of samples prepared at solution cooling rates of 10, 5, and 1 °C/min, respectively, while the dashed lines denote the second heating of samples prepared with cooling rate of 1 °C/min. All the DSC scans were at a heating rate of 1 °C/min.

more phase mixing between the monoclinic and rotator phases. Increased cooling rate has a modest effect on increasing the relative size of the monoclinic solid-solid transition peak. PEB has very little effect on the DSC endotherms, whereas the yield stresses are depressed by 2 orders of magnitude. This demonstrates that the PEBs are not primarily operating by altering crystallization, but by sterically stabilizing wax crystals that do form.7 Figure 10 shows the corresponding DSC scans for C28 alone and with added PEB. The pure C28 sample from the second heating shows two peaks.14-16 With added PEB a third peak appears at a temperature of about 55 °C, which can be attributed to crystallization of the PEB. For the C28 crystals from solution, the pure C28 sample (Figure 10a) shows a merging of the peak associated with metastable phases and the peak associated with the main melting transition. The low-temperature peaks shift about -1 °C with increasing cooling rate. But the dramatic decrease in yield stress with increasing cooling rate is not reflected in a dramatic shift in the phases of the wax crystals. Adding PEBs (Figure 10b,c) causes more complex peak shifts and the appearance of the third peak at lower temperatures. Clearly, the

The rheological characteristics of the paraffin gels formed from long-chain paraffin solutions depend on the cooling rate and the addition of PEB random microcrystalline polymers. The yield stresses of the gels formed by crystallizing long-chain paraffins from solution increase with increasing cooling rates for C36 and C32 waxes, but decrease for C28. The dramatic changes in rheology (a decrease in yield stress by 40% for C28 with increased cooling rate) are not reflected in dramatic changes in DSC endotherms or wax phase behavior. Also, the dramatic decreases in yield stresses upon the addition of PEBs are not reflected in dramatic changes in DSC endotherms. This again points to the importance of colloidal interactions and steric repulsions1,6,7 on the assembly of wax structures that lead to yield stresses. The yield stresses of gels from binary solutions of C36 + C32 and C36 + C28 have yield stresses always smaller than the yield stresses of the single components at the same solid concentration. This can be thought of as a dilution of the strongest gel-forming phase. The morphology of the crystal phases shows minor changes with cooling rate but shows major changes upon addition of PEBs. This is in agreement with the observation that the yield stresses change somewhat with cooling rate but change dramatically upon the addition of PEBs. Addition of PEBs reduces crystal size and changes morphology significantly, effects not markedly dependent on cooling rate. The apparently anomalous behavior of C28 is also reflected in DSC and X-ray diffraction.20 DSC thermograms show two major endotherms upon melting. This is consistent with the existence of complex, multiple rotator phases observed for C28.14-20 The position and size of the first melting peak shift to higher temperatures for slower cooling rates by a small amount (∼1 °C). The phase volume and perfection of the phases would be expected to depend on the kinetics of quenching. Recently, we observed distinct behavior of C28 compared to C32 and C36 by X-ray diffraction for crystals separated from solutions.20 When the cooling rate was decreased from 10 to 1 °C/min, the diffraction from the C28 layered structures showed two sets of peaks with slightly different layer repeat distances, while for C36 and C32 there was only one set of peaks. As a hypothesis, we draw the analogy between the reduction in yield stress for C28 at faster cooling rates and the reduction in yield stress for a mixture of two waxes that crystallize as two distinct phases.17 Further investigations into the origins of the differences between C28 and higher waxes are certainly warranted. Quantifying the phase volumes for the C28 rotator and monoclinic phases could be addressed by microprobe scattering techniques and possibly optical imaging. While we have demonstrated the effects of cooling rate on the yield stresses and structure for paraffins with added microcrystalline PEB polymers, there are certainly a number of problems yet to be addressed. Direct imaging studies of the paraffin crystal faces in the presence of polymer and the nature of the junction between paraffin crystals in the gel would (20) Guo, X.; Pethica, B. A.; Huang, J. S.; Prud’homme, R. K. Prepr. Pap.-Am. Chem. Soc., DiV. Pet. Chem. 2005, 50, 228.

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Guo et al. Acknowledgment. This work was supported financially by Halliburton Energy Services, Inc. We thank Dr. Ian Robb and Dr. David Moore for the GC and IR analyses of the paraffins.

Appendix A

Figure 11. DSC thermographs of solid crystal samples from 4%C28 with various cooling rates. All the DSC scans were at a heating rate of 1 °C/min.

contribute to our understanding and ability to control gelation. Microstructural characterization of wax morphology using X-ray diffraction is the next step in understanding the effect of cooling rate and polymer interactions on structure.

The DSC thermograms in Figures 9 and 10 show irregularities in the shapes of the main peaks. In response to a reviewer’s helpful question, we show duplicate runs for the samples shown in Figure 10a. The locations of the main peaks are identical for duplicate runs, but the irregularities superimposed on those peaks are variable. Note that after remelting the sample (“second heating” on the figure) the peaks are smooth. A possible explanation for the irregularities is because microdomains and metastable microphases are trapped during the initial crystallization. The existence of these metastable phases has been amply discussed.14-16 The differing geometries, phase mixing, and volumes of these trapped domains could give rise to the structure seen in the peaks in Figure 11. Note that the fastest cooling rate gives rise to the most heterogeneity in the peak shape, which is consistent with the proposed mechanism. EF050163E