1. ISSN (Print): 2328-3777, ISSN (Online): 2328-3785, ISSN (CD-ROM): 2328-3793
American International Journal of
Research in Formal, Applied
& Natural Sciences
AIJRFANS 14-246; © 2014, AIJRFANS All Rights Reserved Page 91
Available online at http://www.iasir.net
AIJRFANS is a refereed, indexed, peer-reviewed, multidisciplinary and open access journal published by
International Association of Scientific Innovation and Research (IASIR), USA
(An Association Unifying the Sciences, Engineering, and Applied Research)
Molar volume and rheology of anionic surfactants in non-aqueous media
Suman Kumaria
*, Mithlesh Shuklaa
, and R.K Shuklab
a
Department of Chemistry , Agra College, Agra-282004, India
b
Department of Chemistry ,R.B.S. College, Agra-282004, India
I. Introduction
Surfactants are surface active agents usually organic compounds, characterized by the possession of both polar
and non-polar regions in the same molecule. This dual nature is responsible for the phenomenon of surface
activity, micellization and solublization. The dual nature of a surfactant is typified by metal alkanoates, can be
called association colloids, indicating their tendency to associate in solution, forming particles of colloidal
dimensions.
While major developments have taken place in the study of metal alkanoates of mono-carboxylic acid, the study
of di-alkanoates of di-carboxylic acid is almost untouched. Burrows et al1
synthesized di-carboxylic acid metal
alkanoates by metathesis and Ikhuoria et al2
studied the effect of temperature on the stability of metal
alkanoates of dicaboxylic acids. Suzuki3
prepared and investigated the thermal dehydration of manganese(II)
dialkanoate anhydrides in various atmospheres. Liu et al4
synthesized different metal dialkanoates such as
calcium glutarate, zinc glutarate, calcium sebacate and zinc sebacate and discussed their use as thermal
stabilizers for PVC material. Barbara and Lacz5
studied the thermal decomposition of cadmium butanedioate
dihydrate. A number of workers have reported ultrasonic6,7,9
measurements of metal alkanoates for the
determination of ion-solvent interaction in organic solvents. Viscometric7-9
conductometric9-10
measurements of
lanthanide and transition metal alkanoates have been reported in different organic solvents.
The focus of this paper is to look in to the bulk behavioral aspects like apparent molar volume and
rheology(viscosity/ fluidity) of zinc mono-(hexanoate and decanoate) and di-(butanedioate and hexanoate)
alkanoate by using density and viscosity measurements in a mixture of benzene and methanol (50% v/v) at
30±0.05⁰C.
II. Experimental
All the chemicals used were of BDH/AR grade. Solvents benzene and methanol were purified by distillation
under reduced pressure. Zinc mono- (hexanoate and decanoate) alkanoates were synthesized by direct
metathesis of corresponding potassium alkanoates as mentioned in our earlier publications6,10
, while di-
alkanoates of zinc were synthesized by metathesis in alcohol solution. The zinc di-alkanoates (butanedioate and
hexanedioate) were first prepared by dissolving the dicarboxylic acid in hot ethanol, followed by treatment with
potassium hydroxide solution. To this mixture, solution of the zinc salt was added slowly with continuous
stirring. The precipitated alkanoates of the dicarboxylic acid was filtered off, washed with hot water and air-
dried. The alkanoates were purified by recrystallization with alcohol and dried under reduced pressure. The
purity was checked by their melting points (hexanoate-130.0
⁰
C decanoate-92.0
⁰
C and butanedioate-310.0
⁰
C
hexanedioate-263.0
⁰
C) and absence of hydroxylic group was confirmed by IR spectra. The reproducibility of
the results was checked by preparing two samples of the same alkanoates under similar conditions.
The solutions of zinc mono- and di-alkanoates were prepared by dissolving a known amount of alkanoates in a
benzene-methanol mixture (50% v/v) and were kept for 2 hr in a thermostat at 30±0.05ºC temperature. The zinc
mono- and dialkanoates do not possess high solubility in pure solvents thus measurements were conducted in
benzene - methanol mixture. Densities of the solvent and solution were measured by pyknometer. The
Pyknometer was calibrated with distilled water and buoyancy corrections were applied. Ostwald type
viscometer was used for measuring viscosity (±0.002) of the solutions.
Abstract: The apparent molar volume, and fluidity for the solution of anionic surfactants ie. zinc hexanoate
and decanoate as mono-alkanoates and butanedioate and hexanedioate as dialkanoates in a mixture of
benzene-methanol (50% v/v) at 30ºC have been evaluated from the data of density and viscosity. The value
of CMC decreases with increasing chain length of fatty acid constituent The limiting apparent molar
volume, has been calculated by Masson’s equation.
Keywords: Anionic surfactants, metal alkanoates, density, molar volume, fluidity, rheology.

2. Suman Kumari et al., American International Journal of Research in Formal, Applied & Natural Sciences, 6(1), March-May 2014, pp. 91-
94
AIJRFANS 14-246; © 2014, AIJRFANS All Rights Reserved Page 92
III. Results and Discussion
Apparent Molar volume
The density, ρ of zinc mono-(hexanoate and decanoate) and di-alkanoate (butanedioate and hexanoate) in the
mixture of benzene-methanol (50% v/v) at 30⁰C (Fig.1) is found to increase with increasing solute
concentration, C as well as increasing chain length of alkanoates. The plot ρ-C (Fig.1) of zinc mono-alkanoates
is characterized by an intersection of two straight lines at a critical concentration, CMC (Table I). While the
plots (Fig.1) of di-alkanoates is charatcterized by two breaks at definite solute concentration which corresponds
to the critical micellar concentration, CMC (I) and CMC (II) in dialkanoate solution (Table I). The appearance
of CMC (I) and CMC (II) can be explained on the basis of the formation of ionic and neutral micelles in the
surfactant solution. The concentration at which micelles formation starts known as critical micellar
concentration (CMC), beyond this concentration the bulk properties of the surfactant, such as osmotic pressure,
turbidity, solublization, surface tension, viscosity, ultrasonic velocity and conductivity changes abruptly. If the
micelles are formed in non-aqueous medium the aggregates are called “reversed micelles” in this case the polar
head groups of the surfactant are oriented in the interior and the lyophilic groups extended outwards in to the
solvent. The values of CMC (I) and CMC (II) vary with the chain length of alkanoates molecule which may be
due to the increase in micelle stability and increasing tendency to aggregate. The plots (Fig.1) of density vs.
concentration of solution of zinc alkanoates below CMC have been extrapolated to zero surfactant
concentration; the extrapolated values of density, ρ for these alkanoates are in agreement with the experimental
value of density of solvent mixture. The equation by W.C. Roots11
has been applied to dilute anionic surfactant
solutions below CMC to evaluate the Roots constants11
(A and B). The order: A > B was found, suggest that
the solute-solvent interactions predominate in dilute solutions of zinc alkanoates and micellization only begins
at the CMC.
The density data (Fig.1) are used to evaluate the apparent molar volume, φv (solute-solvent interaction) by
employing equation12
φ
ρ
ρ ρ
ρ ρ
Where M, ρ, ρ0 and C represent the molecular weight of the zinc alkanoates, density of solution, density of
solvent and concentration of the surfactant solution, respectively. It is obvious that increase in surfactant
concentration, and chain length of molecule apparent molar volume φv (solute-solvent) increases (-φv decreases)
below the CMC and the same decreases (-φv increases) above the CMC. The limiting apparent molar volume,
φv
0
has been obtained by extrapolating the linear plot of φv vs. C1/2
and found to be increase with increase in
chain length (Table I) for dilute alkanoates solutions (below the CMC) according to Masson’s equation13
for
electrolytes. φ φ . The limiting apparent molar volume, φ and the experimental limiting
slops, (Table. I) are measures of solute-solvent and solute-solute interactions, respectively. The positive
values of indicates strong solute-solute interactions leading to a fair chance of micellization in these
surfactants solutions. The apparent molar volume, like any other partial molar quantity, expresses the change in
an extensive thermodynamic property per mole of a component is added. The partial molar volumes of ionic
solute usually are smaller than expected. In some cases, it is actually negative in dilute solution. This means that
when a small amount of solid is added to a polar solvent, the volume of the solution is smaller than the volume
of the solvent. The reason is the phenomenon of electrostriction in which smaller cation (Zn2+
ion), with its
strong electric field, packs polar solvent molecules around itself in a smaller volume than they occupy in the
bulk solvent.
Rheology
Rheology deals with the deformation and flow of nature of matter as a result of the exertion of mechanical
forces. The results of rheological behavior provide a mathematical description of the viscous and elastic
behavior of matter. The viscosity, η and fluidity, (reciprocal of viscosity) are considered to be the important
rheological parameters. A major characteristic of liquid is their ability to flow. Highly viscous liquids flow only
very slowly because their large molecules get emerged. Mobile liquids have low viscosities. When ionic crystal
dissolved, the solution consist of a distribution ions supported by the solvent (electrolyte solution). In dilute
solution of zinc alkanoates, the cations Zn2+
ion, and anions, RCOO-
and R(COO-
)2 are so far apart that they
have insignificant interactions, but as the concentration increases anions tend to congregate in the vicinity of the
cations, and vice-versa. The plots of fluidity, of solution of zinc mono-and dialkanoates as a function of
solute concentration, C manifest the cited fact i.e. the fluidity (Table I) decreases (viscosity increases) with
increasing chain length and concentration of alkanoates solution owing to the formation of large entities
(micelles) at higher concentration of surfactant solutions.
The plots (Fig.2) of viscosity vs. alkanoates concentration, (η - C) are characterized by an intersection of two
straight lines at CMC (Table I) in a mixture of benzene-methanol (50% v/v). The viscosity, η of the dilute
solution of zinc surfactants increases with increase in solute concentration which may be due to the tendency of
surfactant molecule to form aggregate (micelle) with the increase in alkanoates concentration in non-aqueous

3. Suman Kumari et al., American International Journal of Research in Formal, Applied & Natural Sciences, 6(1), March-May 2014, pp. 91-
94
AIJRFANS 14-246; © 2014, AIJRFANS All Rights Reserved Page 93
medium. The viscosity for solvent mixture, η0 are evaluated (Table I) by extrapolating η - C plots (Fig. 2) to
zero surfactant concentration. The viscosity data have been interpreted in the light of following well known
equations14-17
proposed by Einstein14
, Moulik15
, Vand16
and Jones-Dole17
. Einstein type plots η - C are used to
evaluate molar volume, of solution of zinc alkanoates (Table I), the values molar volume increases with
increasing in chain length of fatty acid constituent in anionic surfactants. The interaction coefficient, θ was
obtained by employing Vand type plots η η . The values of interaction coefficient, θ
(Table I) were found almost independent of chain length. The values of Moulik’s constants (M and K) were
evaluated from η η vs. C2
plots following the order: K > M (Table 1) indicating the predominance of
solute-solute interactions (good probability of micellization). The values of M (solute-solvent interaction) were
found to be almost constant with increase in chain length. The constants A and B from Jones- Dole’s equation
have been evaluated by employing plots of η vs. . The results (Table I) suggest that solute-solvent
interaction constant, B are larger than the A (solute-solute interaction), suggest that the anionic surfactant
molecules do not aggregate appreciably in the premicellar region (below the CMC) but there is a sudden change
in the aggregation at CMC. This may be attributed to the fact that the aggregation of surfactant molecules boost
up the electrokinetic forces causing more intake of the solvent resulting in the increasing viscosity of the
system. The relative viscosity, η , specific viscosity η and intrinsic viscosity η increases with increasing
chain length of fatty acid constituent recorded in Table I. The intrinsic viscosity η for zinc mono- and
dialkanoates obtained by intercept of the curves of η C vs. C. The values of intrinsic viscosity η increase
with increase in chain length.
It is therefore concluded that the equations by Einstein, Moulik, Vand and Jones-Dole are applicable to dilute
solution of zinc mono- (hexanoate and decanoate) and di-(butanedioate and hexanedioate) alkanoates. The
values of CMC and molar volume of these alkanoates, calculated from these equations are in close agreement.
And micellar and bulk behavior (molar volume, rheology) of anionic surfactants can be explained by using
density and viscosity measurements and also suggest that solute-solvent interaction is predominant in
premicellar region.
Acknowledgements
The authors are thankful to UGC, New Delhi for the financial assistance.
References
[1]. H. D Burrows, H. A. Ellis, M. S. Akanni, Proceedings of the 2nd
European Symposium on the thermal analysis (ed. Dallimore).
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[4]. Yan-Bin Liu, Wei-Qu Liu, Meng-Hua Hou, Metal dialkanoates as thermal stabilizers for PVC:, Polymer Degrad. Stab. vol.
92(8), 2007, pp. 1565-1571 .
[5]. M Barbara, A. Lacz, “Thermal decomposition of cadmium butanedioate dihydrate”. J. Therm. Anal. and Calorimetry. vol.
88(1) , 2007 , pp. 295-299.
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[11]. W.C. Roots “An Equation Relating Density and Concentration”. J. Am. Chem. Soc., vol. 55, 1933, pp.850-851.
[12]. R. De Lisi,, C. Genova, R. Testa, and V. Turco Liveri, “Thermodynamic properties of alcohols in a micellar phase. Binding
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[13]. D.O. Masson , “Solute Molecular Volume in relation to Solvation and Ionization” . Philos. Mag . vol. 8, 1929, pp. 218-235.
[14]. A. Einstein “Eine neue Bestimmung der Moleküldimensionen,” Ann. Phys. vol. 19, 1911 pp. 289–306 , vol. 34, 1906, pp. 591–
592 (erratum).
[15]. S. P. Moulik “Proposed viscosity-concentration equation beyond Einsteins region”, J. Phys. Chem., vol. 72(13) 1968 pp. 4682-
4684.
[16]. V. Vand, “Viscosity of solutions and suspensions”. I Theory, J. Phys. Colloid Chem., vol. 52, 1948, pp. 277-299.
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4. Suman Kumari et al., American International Journal of Research in Formal, Applied & Natural Sciences, 6(1), March-May 2014, pp. 91-
94
AIJRFANS 14-246; © 2014, AIJRFANS All Rights Reserved Page 94
Table: 1. Parameters from density and viscosity measurements of the solutions of zinc alkanoates in the
mixture of benzene-methanol (50% v/v) at 30⁰C.
Parameters Derived from Hexanoate Decanoate Butane
dioate
Hexane
dioate
Critical micellar concentration, CMC
( mol dm3
)
k vs C,
ρ vs C
and η vs C
6.3× 10-3
5.6× 10-3
(I) 3.1×
10-4
(II)
6.3×
10-4
(I) 2.9×
10-4
(II) 6.1×
10-4
Density of solvent,ρ0
( g cm-3
)
ρ vs. C 0.800 0.800 0.809 0.800
Limiting apparent molar volume,φ0
(cm3
mol-1
)
v vs C1/2
-6.88 × 104
-9.12 × 104
-8.21 × 104
-8.40 × 104
Constant, Sv v vs C1/2
3.86 × 107
4.64 × 107
11.41 × 106
11.94 × 106
Viscosity of solvent, η0 η vs C 0.451 0.451 0.452 0.456
Molar volume, Vm
( mol-1
dm3
)
ηsp vs C 77.87 82.67 9.16 × 102
9.43 × 102
Moulik’s constant(M and K) (η/η0)2
vs C2
M=1.09
K=8.09 ×
105
M=1.15
K=7.33 ×
105
M=1.06
K=11.71 × 107
M=1.09
K=13.61 × 107
Constants of Jones-Dole’s equation(A
and B)
ηsp /C1/2
vs C1/2
A=4.69
B=77.76
A=6.03
B=70.20
A=6.47
B=31.00 × 102
A=13.98
B=13.11 × 102
Interaction coefficient, θ 1/C vs
1/log(η/η0)
0.1676 0.1397 0.0159 0.0135
Relative viscosity, ηr (η/η0) 1.0444 1.0467 1.0040 1.0244
Specific viscosity, ηsp (ηr -1) 0. 0444 0. 0467 0. 0040 0. 0244
Intrinsic viscosity,[η] ηsp/C vs C 2.37 3.05 2.39 3.51
Fluidity, (1/η) 2.1277 2.1231 2.2120 2.1692
0.81
0.82
0.83
0.84
0.85
0.86
0 0.0002 0.0004 0.0006 0.0008 0.001
DENSITY,ρ(gml-1)
CONCENTERATION, C×(dm3mol l-1)
Figure:1 Density vs. concentration of zinc alknoates at 30⁰C
Hexanoate
Decanoate
Butanedioate
Hexanedioate
0.455
0.465
0.475
0.485
0.495
0.505
0.515
0.525
0.535
0.545
0 0.0002 0.0004 0.0006 0.0008 0.001
VISCOSITY,η(centipoise)
CONCENTERATION, C×(dm3mol l-1)
Figure: 2 Viscosity vs. concentration of zinc alknoates at 30⁰C
Hexanoate
Decanoate
Butanedioate
Hexanedioate