Characterization of the Solvent Properties of Glycerol

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ORIGINAL PAPER
Characterization of the Solvent Properties of Glycerol
Using Inverse Gas Chromatography and Solubility Parameters
Joel D. Vincent • Keerthi Srinivas • Jerry W. King
Received: 13 October 2011 / Revised: 11 February 2012 / Accepted: 5 April 2012 / Published online: 27 April 2012
� AOCS 2012
Abstract The production of glycerol from the synthesis
of biodiesel has led to a market surplus of this polyhydric
alcohol and additional research to find new applications for
this versatile chemical. This study involves the use of
inverse gas chromatography (IGC) to characterize the
solute–solvent interactions between glycerol and a
homologous series of aliphatic alcohols, in which the latter
components are at infinite dilution in the glycerol, which is
the stationary phase contained in a packed GC column. The
IGC experiments were conducted between 51.5 and 111 �C
for the n-alcohols ranging from methanol to n-butanol. All
of the n-alcohol homologs exhibited positive deviations
from Raoult’s law as based on mole fraction activity
coefficients values ranging from 1.86 to 14.4. The mea-
sured mole fraction activity coefficients of the alcoholic
solutes in glycerol showed good agreement with literature
values, and in some cases with those predicted using
existing theoretical models. The mole fraction activity
coefficients increased going from methanol to n-butanol,
reflecting the change in the alcohol’s cohesive energy
densities relative to that for glycerol. The total solubility
parameter of glycerol calculated from IGC data was found
to be 34.8 MPa1/2 which is in good agreement with that
obtained using Hansen solubility parameter approach
(31.6 MPa1/2). This data can be used to characterize the
solvent properties of glycerol as well as to provide ther-
modynamic data for the removal of the alcoholic solutes
from glycerol.
Keywords Activity coefficient � Alcohols � Glycerol �
Inverse gas chromatography � Solubility parameter
Introduction
Glycerol (1,2,3-propane triol or glycerine) is a polyhydric
alcohol that is produced as a by-product of the transeste-
rification of fatty acids present in fats and oils to yield fatty
acid methyl esters, i.e. ‘biodiesel fuel’ [1]. Glycerol can
also be produced from fats and oils as a by-product of their
saponification process to form soaps [2] and subsequent
hydrolysis to fatty acids [3]. Studies have indicated that
since 1970, the amount of glycerol produced from fats and
oils has increased from 40 million tons to around 144
million tons in 2005 [4]. It has been estimated that 1 ton of
any biomass material containing 2.5 % (by weight) of fatty
acids on transesterification with methanol yields about
946 kg of fatty acid methyl esters, 89 kg of glycerol and
23 kg of unreacted fatty acids [5]. This indicates that there
is a yield of 1 kg of crude glycerol for every 9 kg of bio-
diesel produced glycerol thus is a potential economic credit
in the manufacturing of biodiesel. However with the
increasing market for biodiesel as a fuel worldwide, there
is an excess of glycerol available in world market which
has lowered its economic value substantially from
approximately 1,700$/ton in 2001 to about 550$/ton in
2009 [6].
This abundance of glycerol in the market and its rela-
tively low cost has opened a number of venues for the
application of glycerol in food industries, coatings, lubri-
cants, as a humectant in personal care products and in
separation processes [6]. Glycerol is also used as raw
material in chemical syntheses [7], in medicinal applica-
tions [8] and as a substitute for sweeteners [9]. Though,
J. D. Vincent � K. Srinivas � J. W. King (&)
Department of Chemical Engineering, 3202, Bell Engineering
Center, University of Arkansas, Fayetteville, AR 72701, USA
e-mail: jwking1@uark.edu
123
J Am Oil Chem Soc (2012) 89:1585–1597
DOI 10.1007/s11746-012-2070-6
glycerol cannot be directly used as a fuel due to the pro-
duction of toxic and corrosive polymers of acrolein on
burning, their acetylated derivatives have been used as fuel
additives [10], and glycerol has been used as a boiler fuel.
Despite these potential applications, there is a need to
explore other possibilities for glycerol utilization. One pos-
sibility is to extend the use of glycerol as a bio-renewable
solvent medium. Due to its low toxicity, relatively higher
boiling point and water miscibility, glycerol is a potential
‘‘green’’ solvent [11] with the potential of replacing more
hazardous chemical solvents. Some studies have been
reported using glycerol as a solvent to extract phenol from
coal tar hydrocarbons [12] and for accelerating the rate of a
number of organic reactions. However, there is limited data
on the solubility and miscibility of glycerol, as a function of
temperature, with other organic solvents.
This study seeks to reconcile this lack of data and explore
the relationship between glycerol and a homologous series of
alcohols (methanol, ethanol, 1-propanol, and 1-butanol) at
infinite dilution as a function of temperature. Such thermo-
dynamic data for multi-component systems at infinite dilu-
tion allow on a more fundamental level, the study of
molecular interactions between the alcoholic solutes and
glycerol. A number of techniques have been used to study the
solvent characteristics of glycerol including inverse gas
chromatography [13], differential ebulliometry [14], dew
point techniques [15], steady state and unsteady state gas–
liquid chromatographic and liquid–liquid chromatographic
methods [16]. The inverse gas chromatographic technique
(IGC) has been widely used as a relatively simple and
reproducible technique to measure thermodynamic data of
solutes in vegetable oils [17], polymers [18], biodiesel [19]
and organic solutes [20] as a function of temperature.
In this study, the mole fraction activity coefficients,
Henry’s law constants, heats of solution and vaporization
for the alcoholic-solute interactions with glycerol are
determined at infinite dilution as a function of temperature
between 51.5 and 111 �C using the IGC technique. The
solubility parameter of glycerol as a function of tempera-
ture was also calculated from the physicochemical data
obtained using the IGC technique and verified using the
Hansen three-dimensional solubility parameter approach
[21]. The solubility parameter and the interaction param-
eter values are seminal for studying the solution charac-
teristics and selectivity of glycerol towards the selected
alcoholic solutes. Theoretical solution thermodynamic
models based on solute–solvent interactions, such as the
Miller–Guggenheim method [22] and group contribution
methods, such as UNIFAC [23], have been used exten-
sively in predicting the mole fraction activity coefficient of
various compounds. These calculated activity coefficients
values are compared with those experimentally derived
from the IGC measurements.
Experimental Procedure
Materials
Glycerol (99.7 % pure) was purchased from BDH Chem-
icals (West Chester, PA, USA). Chromasorb G (45/60
mesh, acid washed and silanized, P/N# 25651) was pur-
chased from the Restek Corporation (Bellefonte, PA,
USA). Ultra high pure helium was used as the carrier gas,
and the flame ionization combustion gases, hydrogen and
air, were also purchased from Airgas (Tulsa, OK, USA).
HPLC-grade methanol (P/N# MX0475-1), 1-propanol
(P/N# PX1824-6), and 1-butanol (P/N# BX1780-6) were
obtained from the VWR Corporation (Batavia, IL, USA).
Ethanol (200 proof) was obtained from PharmCo Product,
Inc. (Brookfield, CT, CAT # E200). Chromatographic
injections were made using syringes obtained from the
Hamilton Company (Reno,NV, USA).
Column Preparation
The glycerol chromatographic columns used in the exper-
iments were prepared using 0.5 m sections of copper tub-
ing (0.64 cm o.d 9 0.425 cm i.d). Column packings were
prepared by mixing a selected weight percentage of glyc-
erol dissolved in methanol with the packing material fol-
lowed by solvent removal using a Rotavapor R110 (Buchi
Labortechnik AG, Flawil, Switzerland). The amount of
glycerol precipitated as the stationary phase was measured
by taking triplicate samples of the packed material in
ceramic crucibles and pyrolyzing them in a bench top
muffle furnace (Omegalux LMF A550, Omega Engineer-
ing Inc., Stamford, CT, USA) at 700 �C overnight. The
weight difference before and after pyrolysis was used to
determine the actual weight of glycerol in the stationary
phase. Columns containing weight percentages of 11.2,
17.6, 21.7 and 27.4 % of glycerol were prepared using the
above described method. After packing the coated Chro-
masorb stationary phase support in the columns, they were
equilibrated in the gas chromatographic oven overnight
using a small flow of helium carrier gas to aid in removing
any residual solvent left in the packing material. As a
check, the percentage liquid phase was compared both
before and after use of the IGC columns via the above
pyrolysis technique, the total amount of glycerol lost from
the column varied from 0.95 to 3.28 %.
Inverse Gas Chromatography
The experimental procedure followed in the study is sim-
ilar to that described previously [24, 25]. A column con-
taining a specific weight fraction of glycerol was placed in
a HP 5890 (Agilent Technologies, Santa Clara, CA, USA)
1586 J Am Oil Chem Soc (2012) 89:1585–1597
123
Series II gas chromatograph equipped with a HP 7673 auto
sampler and a flame ionization detector (FID). The flow
rate of the gases was measured at the exit of the FID using
a soap bubble flow meter. The column flow rate measure-
ments were done at ambient temperature and then corrected
to column conditions. The air to hydrogen ratio was
maintained at 6:1 in order to maintain sufficient flame in
the FID sensitivity for detecting the injected solutes under
infinite dilution conditions on the glycerol column.
Approximately 5 ll of methane was injected along with the
solute to measure the column dead volume. The four
alcoholic solutes were injected in triplicate over a given set
of column temperatures: approximately 50, 65, 80, 95 and
111 �C, respectively. The actual column temperatures were
measured using four J-type thermocouples placed at dif-
ferent points in the oven with the signals transmitted to a
Cole–Parmer data acquisition board (Model # 18200-40,
Vernon Hills, IL, USA) and recorded using TracerDAQ
software on a Dell Inspiron laptop computer. The atmo-
spheric pressure was read from a mercury barometer
(Fisher Scientific, Pittsburgh, PA, USA) at 4-hour intervals.
The chromatograms obtained from each injection were
recorded on a desktop computer using Hewlett Packard
Chemstation v. 2.0 software and the data converted to
Excel spreadsheet for further analysis.
Calculations
The theory and the calculations involved in determining the
activity coefficients at infinite dilution of glycerol in the
selected alcoholic solutes and its corresponding solubility
parameter has been described previously [17, 19, 24] and
will only be briefly discussed in this manuscript. The
specific retention volume of the alcoholic solutes in glyc-
erol can be calculated from Eq. 1 as:
V0g ¼
ðtr � taÞð273:16=T0Þð760=P0Þð1 � Pw=P0ÞðjÞðF0Þ
w2
ð1Þ
where, tr, ta are the retention time of the solute (r) and non-
sorbed (dead volume marker) solute (a), T0 is the ambient
temperature, Pw is the vapor pressure of water, P0 is the
atmospheric pressure at ambient conditions, j is the James–
Martin compressibility factor, F0 is the flow rate at ambient
conditions, and w2 is the weight of the stationary phase.
The infinite dilution mole fraction activity coefficient of
the alcoholic solutes in glycerol can be calculated using
Eq. 2 as follows:
ln c1x
� � ¼ ln 273:16R
V0g MP
0
 !
� P
0 B11 � V
� �
RT
ð2Þ
where, P0 is the vapor pressure of the alcoholic solute (i),
B11 is the second pure virial coefficient of the solute, �Vi is
the molar volume of the solute, R is the universal gas
constant and T is the column temperature (K). The value of
P0 was calculated using Antoine’s equation and the
corresponding constants for the different alcoholic solutes
were obtained from the literature [26]. The value of the
second virial coefficient (B11) is usually very small and
often neglected. In this particular study, the values of B11
were found to be lower than the standard error associated
with the experimental data and therefore, was considered
negligible.
The activity coefficient of the alcoholic solutes in
glycerol in mole fraction units calculated using Eq. 2 can
be further converted into the weight fraction activity
coefficient using Eq. 3 as follows:
c1w ¼ c1x
Mi
Msh i
� �
ð3Þ
where, Mi is the molecular weight of the alcoholic solute
and Ms is the molecular weight of the stationary phase, i.e.,
glycerol’s molecular weight.
The variation in the retention volume (Vg
0) and mole
fraction activity coefficient (cw) of the alcohols in glycerol
with temperature can be used to calculate the enthalpies of
solution (DHs
?) and mixing (DHm
?) at infinite dilution as
given in Eqs. 4 and 5, respectively as follows:
DH1s ¼ R
o ln V0g
� �
o 1=T
� �
0
@
1
A ð4Þ
DH1m ¼ R
o ln c1x
� �
o 1=T
� �
0
@
1
A: ð5Þ
The enthalpy of solution of the alcoholic solutes in
glycerol is also related to its enthalpy of mixing and the
enthalpy of vaporization as shown below in Eq. 6:
DH1s ¼ DH1v � DH1m : ð6Þ
The enthalpy of vaporization (DHv
?) is calculated from
the difference between the heats of solution and mixing of
the alcohols in glycerol.
The enthalpy of vaporization of the alcohols was cal-
culated from the Clausius–Clapeyron equation given in
Eq. 7 as:
ln P0
� � ¼ �DH
1
v
RT
þ A ð7Þ
Thus, the DHv
? can be calculated from the slope of the
variation of the natural logarithm of the vapor pressure (P0)
as a function of inverse of temperature. As indicated
J Am Oil Chem Soc (2012) 89:1585–1597 1587
123
previously, the vapor pressures of the alcohols were cal-
culated from the Antoine’s correlation.
The magnitude of the Henry’s Law constant at infinite
dilution H?, can be used to calculate the solute vapor
pressure above the glycerol phase and was calculated using
Eq. 8 below:
H1 ¼ RT
V0g M
: ð8Þ
The alcoholic solute–glycerol interactions can also be
evaluated by calculating the Flory–Huggins interaction
parameters at infinite dilution (v?) as given in Eq. 9. The
critical interaction parameter (vc) can be calculated using
Eq. 10:
ln vtð Þ ¼ ln c1x
� �� ln m1
m2
� �
� 1 þ Vi
M2m2
ð9Þ
vc ¼
1
2
1 þ
ffiffiffiffiffi
m1
m2
r� �2
ð10Þ
where, m1 and m2 are the specific molar volumes of solute
and solvent at a given temperature, T.
The solubility parameter of glycerol, which is the square
root of its cohesive energy density, as a function of tem-
perature, can also be calculated from the IGC retention data
using an Eq. 11 [13].
d21
RT
� v
1
V1
� �
¼ 2d2
RT
� �
d1 � d
2
2
RT
þ vs
V1
� �
ð11Þ
where, d1 and d2 are the solubility parameters of solute and
solvent, respectively, at temperature T and vs is the entropic
contribution to the total interaction parameter of the alco-
hol–glycerol systems. In order to expand the database for
an accurate predictionof the solubility parameter of glyc-
erol, the activity coefficients of other alkanes, aromatics
and chlorinated hydrocarbons in glycerol at the experi-
mental temperatures were obtained from the literature [27].
The entropic contribution to the total interaction
parameter (vs) for the solutes in glycerol can be calculated
from Eq. 12. The solubility parameters of the solutes were
obtained from literature [28] and their variation with
temperature estimated using Eq. 13 [29].
vs ¼ v1 � vH ¼ v1 �
m1 d1 � d2ð Þ2
RT
ð12Þ
and,
d1;T2 ¼ d1;T1
1 � T2
1 � T1
� �0:34
ð13Þ
where, T1 is at 298.15 K and T2 is the experimental tem-
perature in Kelvin.
The total solubility parameter of glycerol (dT) can also
be expressed as a function of the contribution from the
dispersive (dD), polar (dP) and hydrogen bonding (dH)
forces as given by Eq. 14.
d2T ¼ d2D þ d2P þ d2H: ð14Þ
The utilization of the Hansen sphere approach to
estimate the solubility parameter of glycerol has been
discussed in detail previously [19]. The Hansen spheres
based on the interaction of glycerol with various solutes
reported in the literature [30] were plotted using a Hsp3D
program that was kindly provided as a freeware by Dr. Fred
Turner (Western Research Institute, Laramie, WY, USA).
The use of this program to plot the Hansen spheres in order
to predict the solubility parameter of a compound is based
on its interaction with other solvents has been discussed in
detail in the literature [31]. The Hansen spheres can also be
used to characterize the solvent properties of glycerol as
reported previously in the literature [19]. This can be
achieved by comparing the relative energy difference
(RED) values of various solutes in glycerol defined as ratio
of Ra and the radius of the Hansen sphere calculated by the
Hsp3D program (R0). Here, Ra was calculated using Eq. 15
with ‘1’ referring to the solute and ‘2’ referring to the
glycerol.
R2a ¼ 4 dD1 � dD2ð Þ2þ dP1 � dP2ð Þ2þ dH1 � dH2ð Þ2 ð15Þ
The thermodynamic selectivity factors of glycerol for
the four alcoholic solutes are calculated using Eq. 16:
Table 1 Specific retention volumes (mL/g) for glycerol/alcohol systems as a function of temperature
Solute Temperature (�C)
51.5 66.0 81.2 95.8 111
Methanol 232 (±2.30) 115 (±0.25) 65.7 (±0.10) 40.4 (±0.09) 26.1 (±0.10)
Ethanol 190 (±2.34) 98.1 (±0.08) 57.3 (±0.10) 36.4 (±0.10) 21.6 (±0.07)
1-Propanol 220 (±0.98) 110 (±0.34) 59.0 (±0.09) 35.1 (±0.13) 21.3 (±0.53)
1-Butanol 277 (±0.28) 134 (±0.86) 69.8 (±0.26) 39.5 (±1.23) 23.0 (±0.07)
Values in parentheses with ± denote standard deviations from the mean (n = 3)
1588 J Am Oil Chem Soc (2012) 89:1585–1597
123
S ¼ c
i
x
c jx
ð16Þ
where cx
i and cx
j refers to the mole fraction activity
coefficient at infinite dilution of solutes ‘i’ and ‘j’ in
glycerol, respectively. The separation factors, a, between
the various alcohols are calculated using Eq. 17
a ¼ c
i
xP
0
i
c jxP0j
ð17Þ
utilizing the mole fraction activity coefficients and
respective vapor pressures that were previously calculated
for each alcoholic solute.
Results and Discussion
The specific retention times and the retention volume data
for the glycerol–alcohol systems as a function of temper-
ature is given in Table 1. The determined specific retention
volumes for the alcoholic solutes in glycerol over the dif-
ferent column loadings noted previously were in excellent
agreement with each other, indicating that a negligible
influence of the gas–liquid adsorption effect [25] for the
n-alcohols on the glycerol loadings used in this study.
The mole fraction and the weight fraction activity
coefficients calculated using Eqs. 2 and 3, respectively, are
listed in Table 2. It can be seen from the data given in
Table 2 that the alcohol–glycerol mole fraction activity
coefficients changed appreciably with temperature. The
mole fraction activity coefficient of the alcohols in glycerol
were also greater than zero which is indicative of a positive
deviation from Raoult’s law, however, these mole fraction
activity coefficients were small when compared to those for
alkanes, alkenes and alkyl benzenes in glycerol, indicative
that the alcohols exhibit a lesser tendency to escape from
glycerol [27].
The alcohol-glycerol activity coefficient values did
exhibit an increasing trend with the increasing carbon
number of the alcoholic solute as can be seen from the
semi-logarithmic plot shown in Fig. 1. This highly linear
correlation in Fig. 1 can be used for estimating the mole
fraction activity coefficient of other higher carbon number
alcohols in glycerol. This increase in the mole fraction
activity coefficient of the alcohol in glycerol with the
carbon number of the alcohols is indicative of the greater
fugacity of the solute to escape from the glycerol phase. A
similar increase in the mole fraction activity coefficient as
a function of the carbon number is also exhibited by
alkanes and alkyl benzenes in glycerol [32, 33]. These
measured mole fraction activity coefficients were com-
pared with the limited data available in the literature and
with that predicted using theoretical models such as theT
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J Am Oil Chem Soc (2012) 89:1585–1597 1589
123
Universal Functional Activity Coefficient (UNIFAC)
approach [23] and the Martire method using the Miller–
Guggenheim estimation for the ln(cs
?) contribution to the log
of the total activity coefficient, ln(cT
?) [22]. Since the data
available in the literature was limited to 62.4 �C [34] and at
25 �C [35], respectively, the experimentaland theoretically-
predicted values for the activity coefficient at approximately
65 �C are provided in Table 3 for comparison purposes. Also,
the activity coefficient values are listed in Dechema for C1–C6
compounds, namely the values listed for methanol, ethanol,
and 1-propanol in glycerol from 60 to 80 �C [36]. These
values for methanol (2.10–2.12), ethanol (4.06–4.18), and
1-propanol (7.85–8.50) agree well with our experimentally
derived mole fraction activity coefficient values from this
study in Table 3.
However, there was discrepancy between the experi-
mental and the theoretical calculated values of the mole
fraction activity coefficients of the alcohols in glycerol
using the two above described approaches to calculate the
total mole fraction activity coefficient, cx
? for the n-alco-
hols in glycerol. The UNIFAC calculations predicted lower
values for mole fraction activity coefficients of the alcohols
in glycerol when compared to experimental and literature
values in Table 3. Predicted mole fraction activity coeffi-
cients at infinite dilution using, UNIFAC are known to be
unreliable, and it has even been suggested that experi-
mental values of cT
? can be used to evaluate the UNIFAC
parameters. Martire’s method tends to overestimate the
mole fraction activity coefficients for the alcohols (espe-
cially 1-propanol and 1-butanol) in glycerol at 66 �C. For
the Martire method, the predicted activity coefficients are
particularly sensitive to the values chosen for the glycerol
solubility parameters, and hence have a considerable effect
on the thermal contribution to the logarithm of the mole
fraction activity coefficient, ln(cT
?), as well as the overall
mole fraction activity coefficient value, ln(cT). Certainly,
the limited data available for the activity coefficients of
various alcohols in glycerol as a function of temperature
supports the need for the current experimental study.
The variation in the natural logarithm of retention vol-
ume and mole fraction activity coefficient of alcohols in
glycerol with the inverse of the absolute temperature is
shown in Figs. 2 and 3, respectively, and their values are
reported in Table 4. The experimental data conform to an
excellent linear fit for Eq. 4 as indicated by correlation
coefficients which were found to be greater than 0.999. It
can be seen from Table 4 that the heat of solution for
n-alcohols in glycerol varied in the following order: etha-
nol \ methanol \ 1-propanol \ 1-butanol. The heat of
solution is indicative of the energy required to overcome
solute–solvent interactions at a constant pressure. The
current trend indicates that ethanol was a better solvent for
glycerol compared to methanol, 1-propanol and 1-butanol.
The heat of mixing of the alcohols in glycerol did not show
a specific trend with the carbon number of alcohols and
these were very small compared to the heat of solution
values (Fig. 3). Such small heats of mixing indicate that the
selected alcoholic solutes are near-ideal solvents for glyc-
erol and show minimal chemical interaction with glycerol.
This also suggests that the overall solution behavior of the
alcohol–glycerol mixture is athermal with the free energy
of solution being dominated by the entropy of mixing.
The enthalpy of vaporization of the alcoholic solutes in
glycerol as calculated from Eq. 6 is listed in Table 4. As
y = 1.0341e0.6549x
R² = 0.9974
1.0
10.0
100.0
0 1 2 3 4 5 6 7 8
xY
∞
(m
ole
 fr
ac
tio
n)
Alcohol Carbon Number
Fig. 1 Variation of the mole fraction activity coefficient of the
n-alcohols in glycerol as a function of the carbon number of the alcohols
Table 3 Comparison between the theoretical and experimental activity coefficients of n-alcohols in glycerol (cx
?) at different temperatures
Solute cx
?
Experimental (66.0 �C) Martire [34] (62.4 �C) Locke [35] (25.0 �C) UNIFAC [23] (66.0 �C) Martire [34] (66.0 �C)
Methanol 2.02 1.63 1.74 0.631 1.58
Ethanol 4.07 2.98 2.90 1.83 5.83
1-Propanol 7.82 6.18 7.53 3.22 23.2
1-Butanol 14.4 11.4 17.2 5.80 125
1590 J Am Oil Chem Soc (2012) 89:1585–1597
123
indicated in the ‘‘Calculations’’ section, the enthalpy of
vaporization can also be predicted from the slope of the
variation of natural logarithm of vapor pressure plotted as a
function of time as shown in Eq. 7. The theoretically-pre-
dicted DHv
? of the alcohols are also given in Table 4, and
are in excellent agreement with those derived from the dif-
ference in the experimentally-measured values for the heats of
mixing and solution (relative standard deviation of\1 %).
It can be seen from the data provided in Table 5 that the
Henry’s law constants increased exponentially with
increases in temperature, and that the solute volatility
decreased with an increase in the molecular weight of the
alcohols. The high precision of this data in Table 5 as well
as in Table 2 attest to the reproducibility of the experi-
mental method using the HP 5890 gas chromatograph with
automated injection. This data on the Henry’s law con-
stants at infinite dilution can be used in design of desol-
ventizing units and the activity coefficient data in Table 2
is critical for the design of phase separation techniques
such as centrifugation and decantation [37, 38].
The values of the Flory–Huggins parameters of the
alcoholic solutes in glycerol as a function of temperature
and the range of critical interaction parameters are given in
Table 6. The v? values for alcohol/glycerol systems
increased until 66 �C (with the exception of 1-butanol
where the values were constant) and then decreased as a
function of temperature indicating higher miscibility of the
alcohols with glycerol above 66o. The v? values for
alcohol–glycerol systems also increased as a function of
the carbon number of the alcohols at a specific temperature.
It can also be seen from Table 6 that the v? values for
methanol and ethanol were lower than their vc values while
that of 1-propanol was closer to its vc and that of 1-butanol
greater than its vc value as a function of temperature. This
is indicative of the different levels of solubility-miscibility
exhibited by the alcoholic solutes in glycerol which can
vary since this non-ideal behavior is dependent on solute
concentration [39, 40]. It was also found that this is an
opposite trend that was observed for the same alcohols with
a methyl soyate solvent system, where the lower alcohols
showed v? values greater than their respective vc values
and the v? values decreased as a function of the carbon
number [19]. This is indicative of why the lower alcohols
can be better separated from methyl soyate (biodiesel) than
from glycerol after a transesterification reaction [41]. The
v? and vc values calculated as a function of temperature
are also given in Table 6. It was seen that the interaction
0.00
1.00
2.00
3.00
2.
50
2.
60
2.
70
2.
80
2.
90
3.
00
3.
10
3.
20
ln
(γ x
∞
)
1000/T (K-1)
Methanol Ethanol 1-Propanol 1-Butanol
Fig. 3 Variation of the natural logarithm of the weight fraction
activity coefficient for the n-alcohols in glycerol as a function of the
inverse of temperature (1,000 K-1)
Table 4 Comparison between theoretical and experimental heats of vaporization (DHv
?)
Solute DHs
? (Kcal/mol) DHm
? (Kcal/mol) Experimental DHv
?
(Kcal/mol)
Theoretical DHv
?
(Kcal/mol)
% Difference
Methanol 9.08 (±0.4) -0.14 (±0.04) 8.94 8.88 0.64
Ethanol 8.92 (±0.5) 0.37 (±0.05) 9.30 9.38 0.94
1-Propanol 9.73 (±0.2) 0.37 (±0.02) 10.1 10.1 0.16
1-Butanol 10.4 (±0.5) 0.32 (±0.07) 10.7 10.7 0.22
Values in parentheses with ± denote standard deviations from the mean (n = 3)
2.003.00
4.00
5.00
6.00
2.50 2.60 2.70 2.80 2.90 3.00 3.10 3.20
ln
(V
g0
) (m
l/g
)
1000/T (K-1)
Methanol Ethanol Propanol Butanol
Fig. 2 Variation of the natural logarithm of the specific retention
volume (mL/g) for the n-alcohols solutes as a function of the inverse
of temperature (K-1)
J Am Oil Chem Soc (2012) 89:1585–1597 1591
123
parameters of the alcohols in glycerol were smaller than
that for alkanes, aromatics and chlorinated hydrocarbons,
indicating relatively greater miscibility and compatibility
of the alcohols with glycerol.
As noted in the ‘‘Experimental Procedure’’ Section,
Eq. 11 can be used to calculate the solubility parameter of
glycerol at a specific temperature (ex. 111 �C in Fig. 4) and
can be obtained by plotting (d1
2/RT-vi/V1) versus d1 (see
Fig. 4). Figure 4 utilizes data from 24 solute–glycerol
systems and shows an excellent correlation coefficient of
0.955 at 111 �C. Similarly, correlation coefficients of
0.957, 0.956, 0.955 and 0.955 were found at 51.5, 66.0,
81.2 and 95.8 �C, respectively.
The solubility parameter of the glycerol calculated using
Eq. 11 as a function of temperature is given in Fig. 5 and
the solubility parameter value at 25 �C (298.15 K) was
found to be 34.8 MPa1/2 by extrapolation of the linear
relationship. The solubility parameter of glycerol at 25 �C
has been reported in the literature and was found to vary
between 33.8 MPa1/2 [42] and 36.1 MPa1/2 [43]. However,
Table 5 Henry’s law constants (atm) for glycerol/alcohol systems as a function of temperature
Solute Temperature (oC)
51.5 66.0 81.2 95.8 111
Methanol 3.68 (±0.007) 7.59 (±0.001) 13.9 (±0.000) 23.5 (±0.000) 38.0 (±0.000)
Ethanol 3.08 (±0.007) 6.19 (±0.000) 11.2 (±0.000) 18.6 (±0.000) 32.4 (±0.000)
1-Propanol 2.03 (±0.003) 4.21 (±0.001) 8.25 (±0.000) 14.4 (±0.000) 24.7 (±0.002)
1-Butanol 1.31 (±0.001) 2.83 (±0.003) 5.64 (±0.001) 10.4 (±0.004) 18.5 (±0.000)
Values in parentheses with ± denote standard deviations from the mean (n = 3)
Table 6 Flory-Huggins interaction parameters (v?) and critical interaction parameters (vc) for glycerol/solute systems at different temperatures
Solute Temperature (oC) vc
51.5 66.0 81.2 95.8 111
Methanol 0.75 0.83 0.82 0.80 0.78 2.63–2.71
Ethanol 1.40 1.42 1.37 1.31 1.33 2.16–2.22
1-Propanol 2.05 2.06 2.04 2.00 1.98 1.91–1.96
1-Butanol 2.70 2.70 2.67 2.65 2.65 1.74–1.78
Hexane [28] 6.21 6.08 5.96 5.86 5.77 1.39–1.44
Heptane [28] 6.47 6.26 6.07 5.90 5.74 1.41–1.44
Octane [28] 7.01 6.82 6.64 6.48 6.33 1.36–1.38
Nonane [28] 7.43 7.30 7.19 7.09 7.00 1.31–1.33
Decane [28] 7.80 7.63 7.48 7.34 7.22 1.27–1.29
Cyclohexane [28] 4.83 4.59 4.36 4.15 3.97 1.61–1.64
Styrene [28] 4.56 4.21 3.87 3.58 3.31 1.58–1.60
Benzene [28] 3.74 3.59 3.44 3.31 3.19 1.76–1.80
Toluene [28] 4.55 4.30 4.05 3.84 3.64 1.63–1.66
Ethyl benzene [28] 5.07 4.87 4.68 4.51 4.35 1.54–1.56
o-Xylene [28] 4.86 4.62 4.39 4.19 4.00 1.55–1.57
m-Xylene [28] 4.95 4.74 4.53 4.35 4.18 1.54–1.56
p-Xylene [28] 5.03 4.83 4.65 4.48 4.33 1.53–1.56
Tetrachloromethane [28] 5.81 5.47 5.14 4.85 4.58 1.69–1.73
Trichloromethane [28] 3.88 3.68 3.49 3.32 3.17 1.83–1.89
Chlorobromomethane [28] 3.74 3.68 3.62 3.56 3.51 2.02–2.07
Dichloromethane [28] 3.07 2.91 2.74 2.60 2.47 2.03–2.11
Dibromomethane [28] 4.20 4.10 4.00 3.91 3.83 1.99–2.03
1,2-Dichloroethane [28] 3.74 3.61 3.48 3.37 3.27 1.75–1.82
Water [28] -1.42 -1.39 -1.37 -1.34 -1.33 4.50–4.55
1592 J Am Oil Chem Soc (2012) 89:1585–1597
123
the reported values for the solubility parameter of glycerol
were either estimated using empirical models and/or
through functional group contribution methods. One such
approach utilizing Fedors’ group contribution method
estimated the value of solubility parameter of glycerol to
be 33.6 MPa1/2 [44]. As can be seen, the solubility
parameters of glycerol calculated from the IGC retention
data was in good agreement with those reported in the
literature and those that can be predicted using group
contribution methods.
As discussed in the ‘‘Calculations’’ section, the solu-
bility parameter of glycerol was also predicted using the
Hansen sphere approach with the aid of the Hsp3D pro-
gram. The solubility parameter of glycerol, which is
assumed to be the center of mass of the Hansen sphere
shown in Fig. 6a, was found to be dD = 20.5 MPa
1/2,
dP = 14.6 MPa
1/2, dH = 19.1 MPa
1/2. The total solubility
parameter of glycerol calculated using Eq. 14 was found to
be 31.6 MPa1/2. The glycerol solubility parameter esti-
mated using this method, though slightly smaller, was
found to be consistent in magnitude with that calculated
using IGC.
The RED values of common organic solutes in glycerol
as obtained from the Hsp3D program are given in Table 7.
The solubility parameter theory is based on the principle
of ‘‘like dissolves like’’ which means that compounds of
similar solubility parameter values become miscible with
each other. In this regard, the solutes with RED values\1
show good interactions with glycerol while those with
RED [1 showed partial or complete immiscibility in
glycerol. Such poorly miscible solutes are represented by
the dark triangles outside the Hansen sphere and those
miscible are represented by the inverted triangles inside
the sphere in Fig. 6a–c. It can be seen from Table 7 that
mostly alcohols, amines and sulfonated hydrocarbons
showed good compatibility with glycerol while n-alkanes
and chlorinated hydrocarbons were found to be very poor
solvents for glycerol. Salicylaldehyde showed the best
compatibility with glycerol when compared with the
alcoholic solutes. Table 7 indicates that the compatibility
of alcohols with glycerol decreased with an increase in the
carbon number of the alcohols. Moreover, the accuracy of
the above such predictions can be improved by using a
larger database. The IGC technique described in this study
provides one such method that can be used to measure
these thermodynamic properties and hence predict solute–
glycerol interactions.
It is interesting to compare the selectivity factor of
glycerol (Eq. 16) with respect to the four n-alcohol
homologues using the activity coefficient of methanol as
a function of temperature as a baseline, as shown in
Fig. 7. Here the selectivity factor of glycerol for ethanol,
1-propanol, and 1-butanol relative to methanol’s activity
coefficient is in order of the magnitude of their positive
deviation from Raoult’s Law, and the relative selectivity
of glycerol remains fairly constant over a 60 �C tem-
perature range. On the other hand, the separation factor
defined by Eq. 17 which embraces both the solution non-
ideality as reflected in the activity coefficients as well as
their respective saturated vapor pressures, P0, shows
quite a different trend with temperature as shown in
Fig. 8.
At 50 �C, the separation factors for ethanol, 1-propanol,
and 1-butanol are in increasing order with respect to the
carbon number of the alcohol, ranging from approximately
0.82–1.4. Whereas the selectivity factor of ethanol relative
to methanol remains fairly constant over a wide range of
temperature, both the selectivity for 1-propanol and
y = 0.0204x-0.2821
R² = 0.9545
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 5 10 15 20 25 30 35 40 45 50
δ 1
2 /R
T-
i /V
1
(m
ole
/cc
)
δ 1 (MPa1/2)
Fig. 4 Determination of the solubility parameter of glycerol at
111 �C using Eq. 11
y = -0.0264x + 42.673
R² = 0.9967
32.4
32.6
32.8
33.0
33.2
33.4
33.6
33.8
34.0
34.2
34.4
320 330 340 350 360 370 380 390
So
lu
bi
lit
y 
pa
ra
m
et
er
 
o
f g
ly
ce
ro
l (M
Pa
1/
2 )
Temperature (K)Fig. 5 Variation of the solubility parameter of glycerol calculated
from IGC retention data as a function of temperature
J Am Oil Chem Soc (2012) 89:1585–1597 1593
123
1-butanol decreases significantly with temperature in
going from 50 to 111 �C. For 1-propanol, selectivity
decreases from approximately unity to about 0.82, while
for 1-butanol over the same temperature range it
decreases from 1.25 to just under 0.9. These trends
argue for a decrease in selectivity of glycerol for
the higher n-alcohol homologues as temperature is
increased (Fig. 8).
Fig. 6 a Three-dimensional solubility sphere of glycerol plotted using Hsp3D program; b two-dimensional plot of dH versus dD of the Hansen
solubility sphere of glycerol; c two-dimensional plot of dH versus dP of the Hansen solubility sphere of glycerol
1594 J Am Oil Chem Soc (2012) 89:1585–1597
123
Conclusions
The solution thermodynamic data of the selected alcoholic
solutes in glycerol measured using inverse gas
chromatography are indicative of limited molecular solute–
solvent interactions at infinite dilution. The infinite dilution
activity coefficients of the alcoholic solutes in glycerol as a
function of temperature increased as a function of the
carbon number and also showed a positive deviation from
Table 7 RED values of
selected solvents with glycerol
obtained from Hsp3D program
Solvent RED Solvent RED
Salicylaldehyde 0.392 1,4-Dioxane 1.10
Phenol 0.436 Chloroform 1.15
Isopropanol amine 0.511 Trichloroethylene 1.16
Dimethyl sulfoxide 0.622 Tri-n-butyl ketone 1.18
Diethylformamide 0.628 Isoamyl acetate 1.23
Ethylene glycol 0.655 n-Heptyl acetate 1.26
Ethanol 0.690 Di-isobutyl ketone 1.29
n-Propanol 0.752 Chlorobenzene 1.36
Cresol 0.774 Ethyl ether 1.36
Triethylenetetramine 0.770 Dipropylamine 1.41
Isopropanol 0.809 Benzene 1.43
1-Butanol 0.817 Di(2-ethylhexyl) amine 1.45
Propylene glycol 0.820 Carbon tetrachloride 1.51
Cinnamaldehyde 0.826 Cyclohexane 1.56
Pyridine 0.918 Water 1.58
Tertiary amyl alcohol 0.919 Mineral spirits 1.60
Ethyl phenyl acetate 0.969 n-Dodecane 1.60
2-Phenylethyl amine 0.991 n-Decane 1.61
a-Methylbenzylamine 1.00 n-Nonane 1.61
Tetrahydrofuran 1.00 n-Octane 1.62
Acetone 1.01 n-Heptane 1.63
1-Tetradecanol 1.03 n-Hexane 1.65
Methyl isopropyl ketone 1.04 n-Pentane 1.68
Ethyl cinnamate 1.05 n-Butane 1.70
0.60
1.60
2.60
3.60
4.60
5.60
6.60
7.60
8.60
40.00 50.00 60.00 70.00 80.00 90.00 100.00 110.00 120.00
Se
le
ct
iv
ity
 o
f g
ly
ce
ro
l f
or
 a
lc
oh
ol
s 
re
la
tiv
e 
to
 m
et
ha
no
l
Temperature (°C)
Ethanol 1-Propanol 1-Butanol
Fig. 7 Variation in the selectivity factor of the glycerol for n-alcohols
relative to methanol as a function of temperature
0.60
0.70
0.80
0.90
1.00
1.10
1.20
1.30
40.00 50.00 60.00 70.00 80.00 90.00 100.00 110.00 120.00
Vo
la
til
ity
 o
f a
lc
oh
ol
s 
in
 g
ly
ce
ro
l r
el
at
iv
e 
to
 m
et
ha
no
l
Temperature (°C)
Ethanol 1-Propanol 1-Butanol
Fig. 8 Variation of the volatility of n-alcohols in glycerol relative to
methanol as a function of temperature
J Am Oil Chem Soc (2012) 89:1585–1597 1595
123
Raoult’s law, indicating a propensity to escape the glycerol
medium. However, this tendency of the alcohols to volatize
from the glycerol medium was found to be considerably
smaller when compared to alkanes, aromatics and alkyl ben-
zenes activity coefficient values reported in the literature.
From the heat of solution and mixing data obtained from IGC,
it was also seen that the mixing of the solute with the solvent
was greatly dominated by the entropy of the solution with
ethanol and methanol showing better interaction with glyc-
erol. The total solubility parameter of glycerol was calculated
from the IGC retention data as 34.8 MPa1/2 and compared
well to the literature values and that predicted using a Hansen
three-dimensional solubility parameter and Hansen solvation
sphere approach (31.6 MPa1/2). The Hansen solvation sphere
approach was used also used to characterize the solvent
properties of glycerol. The results obtained from the solvation
sphere approach in conjunction with the Flory–Huggins
interaction parameter trends measured from IGC retention
data indicated that the lower alcohols showed greater com-
patibility with glycerol and the interaction decreased as a
function of the carbon number of the alcoholic solutes. These
results can play a significant role in understanding the solvent
properties of glycerol and its application as a ‘‘green’’
renewable solvent [45].
Acknowledgments Joel Vincent acknowledges the University of
Arkansas Honors College for a grant which made this study possible.
We would also like to acknowledge Mr. Harold Watson of the
Department of Chemical Engineering at the University of Arkansas
for his technical assistance during various aspects of this study.
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	Characterization of the Solvent Properties of Glycerol Using Inverse Gas Chromatography and Solubility Parameters
	Abstract
	Introduction
	Experimental Procedure
	Materials
	Column Preparation
	Inverse Gas Chromatography
	Calculations
	Results and Discussion
	Conclusions
	Acknowledgments
	References