Melting points and viscosities of fatty acid esters that are potential targets for engineered oilseed

Article abstract of DOI:10.1007/s11746-007-1159-9

Our previous isolation of branched-chain fatty acid (BCFA) methyl esters from lanolin was improved and scaled up. Also, oleate esters of isopropanol, oleyl alcohol and normal alcohols of 1-12 carbons chain lengths were prepared. Esters were made by interesterification with sodium alcoholates and by esterification with Candida antarctica lipase. It proved easier to obtain pure esters by the enzymatic synthesis. Melting points and viscosities over the range of 0-70 °C were determined in order to better identify potential lubricant targets that might be produced by genetically modified oilseed crops. Isopropyl and butyl oleate have melting points of -33 and -32 °C, respectively and viscosities that range from ~17 cp (0 °C) to ~2.5 cp (70 °C). They should have suitable stability for lubricants. BCFA esters had viscosities similar to their straight chain analogs. Viscosities increased with alcohol chain length and decreased with temperature. The dependence of viscosity on temperature was fit with an equation based on Erying's rate equation. Some esters with branched acid or branched alcohol moieties, and some oleate esters might be utilized as biolubricants or biofuels on the basis of their melting points and viscosities.

Full text of DOI:10.1007/s11746-007-1159-9

J Am Oil Chem Soc (2008) 85:77–82
DOI 10.1007/s11746-007-1159-9
ORIGINAL PAPER
Melting Points and Viscosities of Fatty Acid Esters that are
Potential Targets for Engineered Oilseed
Linxing Yao Æ Earl Hammond Æ Tong Wang
Received: 9 July 2007 / Revised: 28 September 2007 / Accepted: 12 October 2007 / Published online: 14 November 2007
Ó AOCS 2007
Abstract Our previous isolation of branched-chain fatty
acid (BCFA) methyl esters from lanolin was improved and
scaled up. Also, oleate esters of isopropanol, oleyl alcohol
and normal alcohols of 1–12 carbons chain lengths were
prepared. Esters were made by interesterification with
sodium alcoholates and by esterification with Candida
antarctica lipase. It proved easier to obtain pure esters by
the enzymatic synthesis. Melting points and viscosities
over the range of 0–70 °C were determined in order to
better identify potential lubricant targets that might be
produced by genetically modified oilseed crops. Isopropyl
and butyl oleate have melting points of -33 and -32 °C,
respectively and viscosities that range from *17 cp (0 °C)
to *2.5 cp (70 °C). They should have suitable stability for
lubricants. BCFA esters had viscosities similar to their
straight chain analogs. Viscosities increased with alcohol
chain length and decreased with temperature. The depen-
dence of viscosity on temperature was fit with an equation
based on Erying’s rate equation. Some esters with branched
acid or branched alcohol moieties, and some oleate esters
might be utilized as biolubricants or biofuels on the basis of
their melting points and viscosities.
Introduction
Lipids used as lubricants should have suitable viscosities,
low melting points and good stability to oxidation. For
maximum economic advantage they should require only
extraction and limited refining to be ready for use. Low
melting-lipids with good oxidative stability can be
achieved by using esters of monounsaturated fatty acids.
An alternate solution is to use branched-chain fatty acids
(BCFAs) and alcohols. By expressing surface coat genes
that control wax synthesis in oil seed tissue the biosyn-
thesis of such esters might be achieved. Physical property
data for such esters is limited, which prevents rational
target selection. Previously, we reported the melting points
of methyl and isopropyl esters of BCFAs with chain
lengths of 13–18 [1]. Their attractive melting points
encouraged us to measure the viscosity of these molecules,
so we scaled up and refined our previous methods to pro-
duce larger quantities of some branched esters from
lanolin. Methyl oleate melts at -20 °C and has fairly good
oxidative stability [2], which suggests that oleate esters
might be suitable candidates for biolubricants.
In this study, we studied the effect on melting points and
viscosities of oleate esters with alcohols of various chain
lengths and branching.
Keywords Branched chain fatty esters ꢀ Melting point ꢀ
Oleate esters ꢀ Viscosity
Experimental procedures
Materials
L. Yao (&) ꢀ E. Hammond ꢀ T. Wang
Food Science and Human Nutrition,
Center for Crops Utilization Research,
Iowa State University, Ames, IA, USA
e-mail: linxingy@iastate.edu
Lanolin acids were purchased from Rita Corp. (Crystal
Lake, IL, USA) with the brand name-RITALAFA. Silica
gel (40–140 Mesh) was from J.T.Baker (Phillipsburg, NJ,
USA). Lipase acrylic resin from Candida antarctica (EC
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J Am Oil Chem Soc (2008) 85:77–82
3.1.1.3), methyl oleate, oleic acid and alcohols of various
chain lengths, methyl pentadecanoate and methyl palmitate
were purchased from Sigma-Aldrich (St Louis, MO, USA).
Aminopropyl extract-clean cartridges and silica gel G
Uniplates (250 lm) with inorganic binder for thin layer
chromatography (TLC) were purchased from Alltech (State
college, PA, USA).
1.5 h at room temperature. For alcohols with a chain length
longer than 10, the reactants were heated enough to keep
them in a liquid state. The alkali catalyst was generated by
reacting sodium metal with the various alcohols before the
methyl oleate was added. The alcohols were freed of car-
bon dioxide before adding the sodium by sparging with
nitrogen or with reduced pressure. Catalyst was used at
*0.19 mequiv/g of FAME [4]. After the reaction, ade-
quate acetic acid was added to neutralize the catalyst. The
esters were dissolved in hexane and washed with 2%
aqueous sodium bicarbonate solution until the acetic acid
was removed, usually three times. Residual alcohols that
had a carbon chain length less than 5 could be removed by
evaporation under dry nitrogen gas or with a rotary evap-
orator. Longer chain alcohols were mostly removed by
distillation in a water bath at *100 °C and at *0.1 Torr.
Residual alcohol, usually 1–2 ml, was removed by passage
through a silica gel (1 g silica/0.1 g reaction mixture)
column with hexane–diethyl ester (90:10 v/v).
Bench-top Scale-up Procedure for Isolation and
Purification of BCFAs
Methyl esters of lanolin free fatty acids (FFA) were made
by Downing’s procedure [3]. Lanolin FFA was mixed with
benzene, methanol and concentrated sulfuric acid in a ratio
of 5:50:50:1 (g:ml:ml:ml), and refluxed for 4–5 h. The
benzene solution was extracted once with 2% sodium
bicarbonate solution and twice with water. The interme-
diate emulsion phase was separated by centrifugation, and
the benzene solution was filtered through a Buchner funnel
containing sodium sulfate. The benzene was evaporated,
and residual benzene was removed with a stream of
nitrogen gas. The crude FAME was then distilled at
0.5 Torr pressure in a simple insulated still, and the dis-
tillate was collected up to a vapor temperature of 160 °C
using an air condenser to cool the distillate. The distillate
was further fractionated by chain length in a spinning band
column as described previously [1].
Enzymatic Synthesis and Purification of Oleate Esters
When doing transesterifications with a large excess of the
alcohol, it was not economic to remove the residual alcohol
with a silica gel column. To avoid this problem and
improve the purity of products, enzymatic syntheses were
performed with oleic acid and alcohol at a 1:2 molar ratio in
a solvent free system. Candida antarctica lipase was added
at 2% by weight. Molecular sieve in an amount which was
calculated to absorb the water generated in the reaction,
was added at a ratio of 1 g molecular sieve to 1.8 g water at
3 and 24 h after the reaction started. The reaction took
place at room temperature (*25 °C) with constant stirring
and was stopped after 4 days with the addition of water.
The product was centrifuged to remove the enzyme and
molecular sieve, and then extracted with hexane and 2%
sodium bicarbonate solution. Since alcohols were added in
smaller excess than in the chemical syntheses, silica gel
chromatography was applied to the product after extraction
to remove residual alcohol and FFA. If subsequent gas
chromatography (GC) or TLC detected FFA, these samples
were further purified by passing through an amino cartridge
with hexane, and the neutral esters were eluted with chlo-
roform-isopropanol (2:1 v/v).
Urea counter-current distribution of methyl esters was
used to separate branched, normal and hydroxy compounds
with similar boiling points according to their ease of
forming urea complexes [1]. Since *3 g urea is required to
complex 1-g long-chain FAME, we added 6 g FAME
obtained from a spinning band distillation fraction, to a
500-ml filter flask (designated flask #1) and then added 12–
15 g urea and 200 ml of methanol 50%-saturated with
urea. Then the mixture in flask #1 was heated to dissolve
the FAME and urea and slowly cooled it to room tem-
perature for crystallization. A series of 500-ml filter flasks,
each containing 7 g urea, were prepared. A filter stick was
used to transfer the liquid from flask #1 to flask #2. Another
portion of 200 ml 50%-saturated urea–methanol solution
was added to flask #1. The mixtures in flask #1 and #2 were
both heated to dissolve and then cooled to crystallize. This
process was repeated until 15–18 flasks were filled with the
complex. The FAME was released by heating the mixture
at 60 °C, and then extracted with water and hexane.
GC, TLC and NMR
Chemical Synthesis and Purification of Oleate Esters
The purities of oleate esters and BCFA esters were
examined by GC. Esters in hexane solution were injected
into a HP 5890 Series II instrument (Hewlett-Packer, PA)
with a SP-2330 fused silica column (15 m 9 0.25 mm and
Methyl oleate (99% pure) was transesterified with an
excess of the desired alcohol (1:200 molar ratio) for about
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J Am Oil Chem Soc (2008) 85:77–82
79
a 0.20 lm film thickness) (Supelco, Bellefonte, PA, USA).
The injector and flame detector were at 220 °C, and the
oven temperature was programmed from 100 to 220 °C at a
rate of 5 °C/min.
between 0 and 70 °C at 5 °C intervals. Viscosities were
recorded after equilibrating at the desired temperature for
10 min and at the maximum possible torque.
Free fatty acid and residual alcohol also were detected
by TLC on silica plates. Hexane–diethyl ether–acetic acid
(80:20:1) was used as developing solvent. The separation
was visualized under ultraviolet light after spraying with
0.1% (w/v) 20, 70-dichlorofluorescein in methanol.
The structures of the oleate esters in CDCl3were con-
firmed by 13C nuclear magnetic resonance (NMR) with a
Varian VXR-400 NMR spectrometer (Varian Inc., Palo
Alto, CA, USA).
Results and Discussions
Bench-top Scale-up Procedure
The yield of crude methyl ester from the commercial lan-
olin FFA was quantitative based on a MW of 256 for
lanolin FFA and 270 for FAME. They had nearly the same
FAME composition by GC as those of our previous
research [1]. The preliminary distillation removed longer
chain compounds as well as small amounts of sterol esters.
The distillate was rich in FAMEs with chain lengths shorter
than 21 C and the distillation pot residual was rich in
FAMEs with chain length longer than 18 C. Since no new
peaks were observed from GC of the distillate or residual,
we concluded that the distillation did not bring any unde-
sired reaction. The distillate amounted to *38.2% of the
crude FAME by weight. From the crude distillations, 374 g
was collected and fractionated through the more efficient
spinning band column.
Melting Points
Melting points of the oleate esters were measured with a
DSC7 differential scanning calorimeter equipped with an
Intracooler System I (Perkin Elmer, Norwalk, CT, USA).
Indium and n-decane were used for calibration. The melt-
ing onset temperatures of standards were calibrated with
melting points listed in the DSC7 operation manual (Perkin
Elmer, Norwalk, CT, USA). Methyl stearate was used as a
secondary standard, of which the onset melting temperature
(Tonset), peak temperature (Tp), and completion of melting
(Tcom) are 38.9, 41.9 and 43.1 °C, respectively. About 3–
4 mg of each sample was weighed to 0.01 mg in an alu-
mina pan, and an empty pan was used as a reference. The
thermal program was in accordance with our previous
study and AOCS recommendations [1, 5]. After equili-
bration at 25 °C for 1 min, the sample was rapidly heated
to 80 °C at 40 °C/min and held for 10 min for complete
melting of crystal nuclei, cooled to -60 °C at 10 °C/min
rate and equilibrated for 20 min. When reheated at 5 °C/
min, Tonset, Tp, and Tcom were recorded.
The scaled-up counter-current urea separation of the
spinning band fractions yielded gram quantities of methyl
12-methyltetradecanoate (15a) and methyl 14-methylpen-
tadecanoate (16i) with 95% purity. The urea separation also
removed the hydroxy FAME and avoided the expensive
alumina chromatographic purification step used in our
previous study [1].
Oleate Esters Synthesis
Oleate esters of isopropanol, oleyl alcohol and normal
alcohols of 1–12 carbons chain lengths were synthesized
with enzyme as well as with sodium alcoholate catalyst.
The yields of oleate esters by chemical transesterification
averaged 85%, and some batches were as high as 94%. The
purity of the esters by GC was[95%. The major impurity
always was methyl oleate. Enzymatic syntheses gave yields
of *75% but improved the product’s purity to 99% since
the excess oleic acid was easily removed from the non-
polar oleate esters with an amino cartridge or TLC. The
13C-NMR chemical shifts of oleate esters were assigned to
various carbon atoms by comparing observed values with
calculated values obtained by ACD/ChemSketch Predictor
(Advanced Chemistry Development Inc., Toronto, ON,
Canada) and Vieville et al.’s [6] result. The 13C-NMR
spectra of the oleate esters all showed a carbonyl group at
174.4–175.3; the methylene adjacent to the carbonyl group
at 61.5–66.6, except for the isopropyl at 68.3; the
Viscosity
The viscosities of the various oleate esters and BCFA
esters were determined with a Brookfield DV II + vis-
cometer (Brookfield Inc., Stoughton, MA, USA) using a
CP42 cone spindle. The cup was filled with 1 0.03 ml of
ester. Temperature was controlled with an Isotemp 3016
refrigerated circulator (Fisher Scientific, Pittsburgh, PA,
USA). Temperature was monitored with a certified partial
immersion Fisherbrand thermometer (Fisher Scientific,
Pittsburgh, PA, USA) with a range of -1 to 101 °C cali-
brated in 0.1° divisions, which was inserted in a tube on the
return line of the circulating water bath. Air pressure was
used to keep the water level in the tube at the proper
immersion level of the thermometer. Data was collected
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J Am Oil Chem Soc (2008) 85:77–82
methylene b to the carbonyl at 35.1–35.8, double bond
carbons at 130.3–131.3; terminal methyl groups at 11.2–
15.4 except for the isopropyl ester at 22.9; a carbon a to the
terminal carbon at 14.7–15.6, a carbon b to the terminal
carbon at 23.2–24.1; a methylene carbon adjacent to the
ester bond at 61.5–66.6 for the normal chains and 68.4 for
the isopropyl ester; other methylene carbons ranged from
23.7 to 33.3. In most instances the extreme values for the
straight-chain esters belong to the ethyl, propyl or butyl
ester values, which is undoubtedly a reflection the terminal
groups of the alcohols.
Fig. 1 Effect of chain length on the melting points (Tcom) of oleate
esters
Melting Point
then an increasing value (Fig. 1). Literature values of
corresponding esters of various saturated fatty acids as well
as FFAs show similar melting patterns, but at considerably
higher temperatures than the oleate esters [8, 9].
The esters from enzymatic synthesis were used for melting
points measurements since they had higher purity than
those of alkali catalyzed reaction. The melting points of
oleate esters are shown in Table 1. Of all the esters
examined, the lowest melting point was that of isopropyl
oleate at -33.0 °C. Among even chain normal alcohols,
butyl oleate melted lowest at -31.7 °C; and among the odd
chains, propyl oleate was lowest at -27.2 °C. Pentyl and
hexyl oleate’s melting points were very close at -25.2 and
-25.8 °C, respectively. The equipment manufacture’s
precision claim is better than 0.1%, and temperature
accuracy is 0.1 °C; however, the AOCS has reported that
the standard deviation of determination among laboratories
was 1.8 °C for the onset temperature and 0.8 °C for the
completion [5]. The melting points of methyl through
pentyl oleate agreed with the results of Candy et al. [7].
Plots of the melting points of the straight chain ester versus
the number of carbon atoms in the alcohol moiety showed a
decreasing melting point until carbon number four, and
King and Garner gave an explanation on the melting
point pattern of saturated fatty acids [8, 10] based on
crystal diffraction studies and heats of melting. According
to this explanation, the terminal methyl and carboxyl
groups in crystals of fatty acids actually are further apart
than in the liquid state. Thus, when a crystal melts, these
terminal groups come closer together, and their melting is
exothermic. The crystal is held together by the sidewise
attraction of methylene groups in the fatty acid chains, and
their melting is endothermic. The methylene group attrac-
tion increases with the number of these groups per
molecule. As the alcohol chain lengthens from methyl
through butyl, the additional methylene groups make the
end groups take more and more unfavorable positions in
the crystal, making the crystal less stable and lowering
their melting point. In esters with alcohol groups greater
than butyl, the methylene groups have increasing attrac-
tion, and their attraction is greater than the effect of the end
groups. So the crystal stability and melting point begin to
increase as the alcohol chain grows longer. The same
theory could apply to oleate esters.
Table 1 Melting onset (Tonset), peak (Tp) and completion (Tcom
temperatures of oleate esters
)
Alcohol moieties
Tonset (°C)
Tp (°C)
Tcom (°C)
Methyl
Ethyl
-20.3
-23.1
-32.5
-35.7
-29.2
-30.3
-18.3
-9.3
-17.3
-19.0
-28.3
-32.8
-26.3
-27.0
-14.7
-4.1
-16.3
-18.1
-27.2
-31.7
-25.2
-25.8
-13.1
-2.9
Viscosity
Propyl
Butyl
The esters from enzymatic synthesis were used for viscosity
measurements since they had higher purity than those of the
alkali catalyzed reaction. The viscosities of oleate esters
with normal alcohol chain lengths of 1–10 and BCFAs, plus
branched isopropyl oleate in the temperature range of 0–
70 °C are given in Table 2. The melting points of the
methyl esters of BCFAs were reported in a previous paper
[1]. Methyl esters of 15a and 16i melt at -9 and 16 °C,
respectively. Although the melting point of these branched
derivatives are not particularly low, they were chosen for
Pentyl
Hexyl
Heptyl
Octyl
Nonyl
Decyl
-9.4
-5.6
-4.4
2.8
6.8
8.2
Dodecyl
Oleyl
12.9
17.3
18.4
-7.1
-2.9
-1.5
Isopropyl
-37.7
-34.2
-33.4
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J Am Oil Chem Soc (2008) 85:77–82
81
Table 2 Viscosities of oleate esters, BCFA methyl esters and saturated straight chain FAME
Temperature (°C) Viscosity (cp)
Methyl Ethyl Propyl Butyl Pentyl Hexyl Heptyl Octyl Nonyl Decyl Isop
15a 15n 16i
16n
0.00
12.30
10.20
8.64
7.39
6.37
5.66
4.97
4.39
3.91
3.50
3.17
2.87
2.62
2.40
2.21
13.60 15.70
11.30 13.00
9.60 10.95
17.20 19.20 21.80 25.00
14.10 15.65 17.80 20.20
11.80 13.00 14.70 16.60
9.98 10.95 12.30 13.90
27.45 30.60 34.60 15.40 7.97
22.25 24.60 27.70 12.60 6.85
18.20 20.10 22.50 10.50 5.90
–
–
–
–
–
–
–
–
–
–
–
5.05
–
10.00
14.95
20.00
25.00
30.00
35.00
40.00
45.00
49.95
54.95
59.80
64.80
69.70
9.86
8.33
8.17
7.05
6.25
5.48
4.83
4.30
3.84
3.46
3.14
2.85
2.62
2.42
9.25
7.96
6.98
6.08
5.36
4.75
4.24
3.80
3.43
3.12
2.84
2.62
15.20 16.70 18.60
12.80 14.30 15.55
11.10 12.10 13.30
9.53 10.40 11.40
8.89 5.11
8.55
7.48
6.52
5.75
5.08
4.54
4.10
3.69
3.34
3.04
2.78
9.32 10.40 11.70
7.63 4.48 5.05 7.06
6.57 4.03 4.42 5.96
8.23
7.15
6.25
5.50
4.88
4.39
3.92
3.56
3.22
2.95
9.12 10.15
7.88
6.89
6.05
5.36
4.78
4.26
3.84
3.49
3.19
8.77
7.63
6.67
5.88
5.23
4.68
4.18
3.79
3.46
5.67 3.61 3.91 4.94 4.48
4.98 3.22 3.49 4.31 3.94
4.40 2.91 3.11 3.79 3.53
8.30
7.27
6.39
5.67
5.06
4.55
4.11
3.71
9.03
7.89
6.95
6.15
5.51
4.91
4.44
4.00
9.91
8.62
7.54
6.64
5.91
5.28
4.76
4.29
3.89 2.65 2.8
3.36 3.14
3.50 2.42 2.54 3.03 286
3.15 2.22 2.32 2.75 2.6
2.86 2.05 2.13 2.49 2.38
2.59 1.89 1.96 2.29 2.19
2.38 1.76 1.81 2.11 2.02
15a, 12-methyltetradecanoic acid methyl ester; 15n, pentadecanoic acid methyl ester; 16i, 14-methylpentadecanoic acid methyl ester; 16n,
hexadecanoic acid methyl ester; isop, isopropyl oleate; the viscosities of 15n, 16i, and 16n were measured above their individual melting points
fit the experimental data, which gives a very slightly
curved line for ln g versus 1/T. We considered that the fit
for long linear molecules such as oleate esters might be
improved by considering the spatial orientation of the
activated molecules as in Erying’s rate equation [13]. This
equation is often simplified by assuming changes in
entropy for the activated state are negligible. Then
comparison with the oleate esters. The viscosities of
dodecyl oleate and oleyl oleate were not measured because
of limited amounts of materials. Viscosity increased with
the chain length of the esterified alcohol and with
decreasing temperature. The viscosity of the branched iso-
propyl oleate was close to its straight chain counterpart,
propyl oleate. The branch on the alcohol moieties does not
affect viscosity very much. This agrees with Knothes’s
study [11]. Viscosities of methyl esters of 15a and 16i had
viscosities close to those of their straight chain counterparts
as well as that of isopropyl oleate. Such branches on the acid
moieties of these esters did not greatly affect the viscosity.
The oleate esters and BCFAs methyl esters all behave
like Newtonian fluids. At 25 °C, the viscosities remain
constant with an increasing shear rate from 20 to 200 rpm.
Numerous equations have been proposed to fit the
change in viscosity with temperature [12]. Many of these
equations are based on the idea that energy of activation
has to be added to the molecules of a liquid for them to
flow past each other. Such equations are analogous to the
Arrhenius equation for the rate of a chemical reaction and
take the form:
ꢀ
ꢁ
R
Ea
ln g ¼ ln
þ ln T ꢁ
ð2Þ
Nh
RT
where N is Avogadro’s number, and h is Planck’s constant.
The fit of the logarithm of the viscosity data was
improved by the inclusion of the ln T term, but the fit was
still imperfect. By using our viscosity data and appropriate
values of R, N and h, we were able to calculate Ea at the
various temperatures for our esters. Such a treatment
revealed that Ea was not a constant but was almost a linear
function of T. Further study showed that the fit of the data
by this linear equation, like that of Eq. [1] was poorer at the
extreme temperatures and that the fit could be improved
from R2 = 0.9999 to 1 by using a polynomial, such that
Ea ¼ B þ CT þ DT2
where B, C and D are constants. Thus,
ð3Þ
Ea
ln g ¼ ln A ꢁ
ð1Þ
RT
ꢀ
It may be that for long linear molecules such as these esters,
ꢁ
ꢂ
ꢃ
R
B þ CT þ DT2
ln g ¼ ln
þ ln T ꢁ
ð4Þ
where g is the viscosity and A is a constant, Ea is the energy
of activation, T is the temperature in degrees Kelvin and R
is the gas constant. Ln g calculated by versions of this
equation gives a straight line for ln g versus 1/T that poorly
Nh
RT
Ea is a function of T because as temperature increases, the
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J Am Oil Chem Soc (2008) 85:77–82
An example of the fit of decyl oleate data is given in
Fig. 2. Thus, these equations allow prediction of the vis-
cosity at other temperatures and longer chain lengths. This
equation was developed for the oleate esters of straight-
chain alcohols, but fit equally well for isopropyl ester, and
the methyl esters of BCFAs. The equations for isopropyl
oleate, methyl esters of 16i and 15a, respectively, are:
Ea ¼ ꢁ38561 þ 445:57T ꢁ 0:1632T2
Ea ¼ ꢁ53717 þ 541:21T ꢁ 0:3103T2
Ea ¼ ꢁ30266 þ 408:02T ꢁ 0:117T2
ð6Þ
ð7Þ
ð8Þ
Acknowledgments We acknowledge James Cornette for advice
about the viscosity equation, and to the Center for Crops Utilization
Research and the Plant Science Institute at Iowa State University for
financial support.
Fig. 2 Fit of observed viscosity data of decyl oleate at various
temperatures with calculated data of Eqs. 2 and 5. Triangle observed
data, filled circle calculated data
probability of the molecule departing from linearity
increases. Departure from linearity entails a corresponding
increase in the energy needed to move one molecule past
another. This equation’s DT2 term also succeeded in fitting
the curve of the experimental ln g versus 1/T data.
The fit of data by Eq. 4 is not strongly dependent on the
absolute value of ln[R/(Nh)], as B, C and D can change to
make the equation fit when various values of this constant
are used. We used 28.3651 for ln[R/(Nh)] when g was in
centipoise.
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Plots of B, C, and D versus n, the chain length of the
alcohol portion of the esters are generally linear functions
but show considerable scatter. This may be the result of
varying amounts of impurities in the preparations that we
could not detect by the methods we used. Alternatively this
scatter may reflect differences in the favored configuration
of the various esters possibly reflecting the interplay of
methylene and end groups noted by King and Garner [8, 9]
in melting points. However, the errors caused by scatter in
the B, C, and D plots are relatively insignificant. If one fits
these plots with the best straight line for the three plots one
gets the following equation:
Ea ¼ ꢁð833:31n þ 33089Þ þ ð3:1648n þ 419:28ÞT
ꢁ ð0:0039n þ 0:1297ÞT2
ð5Þ
where n is the chain length of the alcohol in the oleate
esters. Using this equation to obtain Ea and substituting it
in Eq. 2 allow one to calculate the viscosity of the esters
with less than 1% deviation from the experimental value.
The fit is worst for the 0 °C values but even these values
differ from the experimental values by an average of 2.2%
and do not exceed 4%. The viscometer has an error of 1%
under the conditions used for our measurements.
123