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Acoustic spectroscopy of aqueous solutions of bis-quaternary ammonium ampholyte
Acoustic spectroscopy of aqueous solutions of bis-quaternary ammonium ampholyte V.S. Sperkach, V.G. Makarov
a n d L.D. K a c h a n o v s k a y a
Institute of Bio-Colloid Chemistry of the Ukrainian Academy of Sciences, 42 Vernadsky Avenue, Kiev 252680, Ukraine
Received 22 September 1993; revised 1 December 1993 Aqueous solutions of surfactants are characterized by the existence of a wide range of relaxation processes. The paper reports on experimental results obtained with aqueous micellar solutions of bis-quaternary ammonium ampholyte by acoustic spectroscopy. Parameters of two relaxation processes lying in the frequency range above 5 MHz were determined, and their probable molecular mechanisms are discussed, The model offered for the description of a fast process (local order restructuring of a network of weak intermolecular bonds) was used to calculate thermodynamical potentials of the reaction and its transmission coefficient.
Keywords: bis-quaternary ammonium ampholyte; micellar solutions; relaxation processes; intermolecular bonds
It is commonly known that surfactant molecules in aqueous solutions form aggregates (micelles) of different shapes and dimensions ,depending on concentration, temperature and other coladitions. Structural transitions between distinctly shaped aggregates are possible under certain conditions and are accompanied by significant changes in physical properties of the solutions. Since surfactant solutions have many practical applications in the different fields of technology, it would be of interest to study structural, physical and thermod.ynamical properties of water-surfactant systems. The investigations of aqueous solutions of tetraalkylammonium compounds and cationic surfactants with trimethylammonium headgroups have previously been carried out by different methods l'z. We have studied aqueous solutions of bis-quaternary ammonium ampholyte (derivative of ethylene-diamine) by ultrasonic relaxation spectroscopy. The surfactant selected possesses high solubility and good surface-active properties, as well as bactericidal and anti-static action. The aim of our investigation was to determine the concentration and temperature relationships of ultrasonic parameters. J
Experimental details The general formula of the bis-quaternary ammonium ampholyte studied is [R-OC(O)CHzN(CH3)2CHzCHzN(CH3) z CHzC(O)O-R] 2 + • 2CIwhere R is a C~o-alkyl radical. The compound was synthesized in the laboratory according to the method 0041 - 624X/ 94 / 06 / 0467-05 © 1994 Butterworth-Heinemann Ltd
of Denisenko and Lopushansky a and was purified by re-crystallization until it was at least 99.5% pure. The solutions were prepared at 293 K by the weight method, with concentrations from 0.010 to 0.300 mole litre- 1. The density of the solutions (p) was determined with a picnometer; the total error amounted to 0.05%. The coefficient of shear viscosity (qs) was measured with a capillary viscosimeter having about 1% accuracy. The experimental technique and the apparatus for ultrasonic measurements have been described elsewhere4'5. The amplitude coefficient of the sound absorption (~) was determined by the pulse method with a variable pathlength in the frequency range extending from 10 to 2800MHz. The measurement error was 2-5% for different frequency values. The velocity of sound (c) was measured at 1 0 M H z with 0.1% accuracy. Additional investigations have shown that dispersion of the sound velocity over the frequency range studied does not exceed 0.1%.
Results and discussion The experimental results obtained are summarized in Table 1. The temperature dependencies of sound absorption, as well as data for some intermediate solution concentrations, are available from the authors. Experimental results have been discussed in part earlier 6. It was established that in relatively dilute solutions (with ampholyte concentrations below 0.100 M) no acoustic relaxation processes were observed in the frequency range studied. The amplitude coefficient of the sound absorption (~) at all temperatures was directly
Ultrasonics 1994 Vol 32 No 6
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Acoustic spectroscopy of bis-quaternary ammonium ampholyte: V.S. Sperkach Table 1
et al.
Physical and structural relaxation parameters of ampholyte solutions Sound attenuation x l O 15 (m lS2)
Solution
(moll
1)
T
p
(K)
(kgm
2
3
1
3)
qs
c
(mPas)
(ms
4
tlv/tls
1)
A
B
:%.f 2
6
7
8
5
9
rps x 1012
zr × 10 9
(s)
(s)
10
11
Water (q'~ - 0)
283 293 313 333 353
999.6 998.1 992.2 983.2 971.8
1.30 1.02 0.68 0.51 0.40
1447 1483 1529 1550 1554
34 25 16 11 9
11.3 8.2 5.1 3.6 2.9
2.7 2.7 2.8 2.8 2.8
2.5 1.9 1.2 0.9 0.7
0.05 (~b - 0.028)
283 293 313 333 353
1001.2 999.8 993.7 984.3 972.1
1.60 1.23 0.82 0.60 0.47
1450 1486 1532 1550 1552
42 32 19 13 11
13.8 9.9 6.1 4.3 3.4
2.7 3.0 2.8 2.6 3.0
3.1 2.4 1.5 1.0 0.9
0.10 (0 0.056)
283 293 313 333 353
1002.4 1000.9 994.7 985.2 973.2
1.93 1.50 0.99 0.71 0.55
1453 1490 1535 1550 1552
51 12
39 33
16.5 11.9 7.2 5.1 4.0
5.1 3.7 3.3 3.6 3.7
2.9 2.5 1.9 1.5 1.2
6.9 4.5
0.15 (q5 _ 0.084)
283 293 303 313 333
1004.5 1002.5 999.7 995.9 986.5
3.00 2.11 1.57 1.23 0.86
1457 1492 1518 1527 1544
56 34 22 16
54 35 31 24
27,0 16.6 12.0 9.1 6.2
4.1 4.2 4.4 4.5 4.5
3.9 2.6 2.4 1.9 2.1
12.2 9.9 8.4 6.9
0.20 (4) = 0.112)
283 293 303 313 323 333
1005.4 1003.8 1001.1 997.4 992.7 987.4
7.56 4.19 2.60 1.78 1.33 1.06
1467 1493 1513 1527 1537 1541
210 90 52 35 19 16
45 37 26 23 19 18
62.6 33.0 18.3 13.3 9.3 8.8
4.1 4.0 4.3 4.3 4.3 4.3
2.9 2.2 1.9 1.6 1.6
19.9 120 10.5 9.8 8.2 6.5
0.30 (4) - 0.168)
293 303 313 323 333
1006.2 1002.8 998.7 993.9 988.7
43.80 15.97 7.35 4.00 2.57
1504 1516 1527 1530 1535
670 305 115 63 30
66 41 35 30 26
383.0 120.0 54.0 30.0 18.9
1.2 2.4 2.4 2,7 2.7
2.4 2.0
31.8 25.7 19.9 16.9 14.5
-
proportional to the frequency squared. No dispersion of sound absorption was observed. From the comparison with data for pure water it is seen that ampholyte solutions possess excessive sound absorption, which increases sharply with surfactant concentration. This means that the introduction of organic electrolyte molecules results in substantial deformations of the water structure, which in turn enhances different restructuring processes (so-called volume viscosity manifestations). The process of the solution restructuring during acoustic wave propagation takes up finite time, i.e. volume changes are shifted in phase with respect to pressure changes in the system, which causes energy dissipation 7. The value of sound absorption determined by the shear viscosity (the so-called classic absorption) could be calculated by a known equation 7 :z~l.]'' 2 = 2 6 . 3 q ~ p
lc
3
(2)
The resulting values are listed in Table 1. It is seen from Table 1 that in dilute solutions the experimental values of the sound absorption are considerably larger than the calculated values of :tj 2 The relation of ~ f 2 > ~ L [ - 2 signifies that the excessive
468
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1994 Vol 32 No 6
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sound absorption which we detect in the given frequency range relaxes at still higher frequencies at least in the Gigaherz range. It should be noted here that the general appearance of the temperature dependencies of the above-mentioned parameters for dilute solutions of the ampholyte coincides with the relationships obtained earlier for pure water ~. The absence of the acoustical relaxation manifestations at frequencies below 2.8 G H z means that the intrinsic time of the processes, which determines volume and shear viscosities of the dilute solution, does not exceed 10 ~1 s. This value corresponds in its order of magnitude to the relaxation time of the fastest process observed in liquid water, i.e. the recombination of hydrogen-ions and hydroxyls. For such a reaction, the relaxation time of the volume and shear viscosities should be calculated by the equation ~
I ~c~
(1)
T h e r a t i o o f the c o e f f i c i e n t s o f v o l u m e t o shear v i s c o s i t i e s (~1,,~1~ ~) is defined as
q,,q~ i = 4./3(:z - ~cl)~cl I
25 19 15
rp,
2~.f 2 c
(31
where c o is the velocity of sound at u)z << 1. As we have mentioned, the dispersion of the sound velocity does not exceed 0.1%, so we could assume c o = c. The values of rp, are listed in Table 1. As is seen, the relaxation time increases with increasing solution concentration. This observation seems to indicate that water molecules belonging to hydration shells of the organic electrolyte molecules possess reduced
Acoustic spectroscopy of bis-quaternary ammonium ampholyte: V.S. Sperkach et al. molecular mobility and low velocity of local order restructuring in comparison with the bulk water. As we have mentioned, the acoustical parameters of the dilute solutions turned out to be rather similar to those of water a. By analogy with water, we could assume that the excess sound absorption in the solutions is caused by local order restructuring processes. In such a case, interpretation of the results obtained could be carried out within the framework of a model implying that any arbitrarily chosen macroscopic unit of the solution, taken for consideration in a time period close enough to its relaxation time, should be treated as a dynamic three-dimensional system with molecules connected by weak (such as hydrogen) bonds. The energy fluctuations which emerge due to the thermal motion of the molecules are sufficient to break one or several such bonds. Nevertheless, under thermodynamic equilibrium conditions the number of the broken bonds is equal to the number of the newly formed ones. Now consider a propagation of the sound wave through the solution. The equilibrium is displaced and relaxation processes emerge in the system, resulting in energy dissipation. On the molecular level it means that several bonds (such as O H . . . O, C H . . . O, O H . . . N) are broken, and the parts of the macroscopic system previously connected by these bonds are displaced so that all broken bonds could not restore after the wave has passed. This process is then considered to be a result of a normal reaction, which is a linear combination of all possible monomolecular reactions, accompanied by changes in the total number of weak bonds in the system
viMi , K, , ~. vjMj i
K
i
(4)
j
where the left and right parts of Equation (4) represent a certain volume of the solution before and after the passage of the sound wave, and differ in the number of intermolecular bonds; vi and vj are stoichiometric coefficients; K 1 and K _ 1 are the corresponding rate constants of the forward and backward Reaction (4). If Reaction (4) is not a collective one, we can write the equation for the relaxation time as
z7 1 = Klnl(1/nl + 1/n2) = K 1 + K_ 1
(5)
where n 1 is the number of bonds in the unit volume of the unperturbed solution, and r/2 is a number of bonds broken in the volume as a result of the sound wave passage. If the perturbation is weak enough and a deviation from the equilibrium state is small, we can assume that Kin1 = K_ ln2 . In the case of the acoustical spectroscopy of liquids, when perturbation is induced by
T a b l e 2 Thermodynamical potentials of the reaction of weak intermolecular bonds breakage in water-ampholyte systems Ampholyte concentration (molel 1)
AH* (kJmole 1K 1)
AS'~o p ( J m o l e 1)
AS* (Jmole
Water 0.025 0.050 0.100 0.1 50 0.200
18.6 16.6 14.7 1 5.1 14.9 1 6.5
14.0 5.9 -1.5 -0.2 - 7.5 -4.8
70 63 55 56 49 51
1)
a low-energy sound wave, we can assume nl >> n2, and consequently, K_ 1 >> K r For a consecutive process the limiting stage has the smallest rate constant, so from Equation (5) it follows that K_ 1 = r~-1. According to Shakhparonov 9, the rate constant for a reaction of hydrogen bond breakage could be written in the following form
K_ 1 = 4~zexkRTexp (-AG* ~ \ RT/ h
(6)
where ~cis the transmission coefficient of Reaction (4), ka and h are Boltzmann and Planck constants, and AG* is the free enthalpy, of activation of the bond breaking reaction. After writing the Gibbs free activation energy change in the form A G * = A H * - T A S * , where AH* is an activation enthalpy and AS* is the activation entropy of Reaction (4), we derive AH* = R
c~ln(K_lT -1) c3(T-1)
(7)
So, substituting z~- 1 for K_ 1, and assuming 4~e~- = 1 as a first-order approximation, we can use previously obtained data for the calculation of the apparent values of entropy (AS*pv) and the activation enthalpy of Reaction (4). The resulting thermodynamical parameters are listed in Table 2. Analysis of the data obtained has shown that in diluted ampholyte solutions (up to 0.100 mole litre-1), for the reaction of intermolecular bond breakage, the kinetic compensation effect is observed AH* = a + bAS*pp
(8)
where a and b denote empirical constants. The deviation from the linear correlation in solutions of 0.150 M and more is induced by the appearance of another relaxation process at low temperatures. Because of this, we could not determine AH* values of the first process by Equation (7) as precisely as before. According to Reference 7 R In (4~eK) = - a/b
(9)
so we can determine the true values of entropy and free activation enthalpy by the relationships AS* = ASa*p - R In (4geh-)
(10)
AG* = AGa* p + RTln(4neK)
(11)
The resulting values are also listed in Table 2. We can use Equation (9) to calculate the value of the transmission coefficient, which turned out to be ~" = 2.0 x 10 -5 . This value coincides, to an order of magnitude, with the coefficient values described in the literature for organic liquids characterized by weak intermolecular bonds, such as alcohols 1°. In solutions of 0.100 M concentration and higher, the frequency dependence of the sound absorption appears, which means that the acoustic relaxation process is observed in the system. In concentrated solutions at low temperatures (below 293 K) continuous relaxation spectra were observed, without any distinctly separated processes, and in all the other cases just one isolated process was determined. The sound absorption for such a process is described by the equation v ~f-2 _
A 1 + (09z2)2
+ B
Ultrasonics 1994 Vol 32 No 6
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469
Acoustic spectroscopy of bis-quaternary ammonium ampholyte: V.S. Sperkach et al. G u t h - S i m h a equation for the dilute dispersions of spherical particles 11 qrel = 1 + 2.5~b + 14.1q52 .o=
2
~
1
0
II
I
III
'
o
o 0.05 o'.a o.is 0'.2
o. 5
~unpholyte concentration (M) Figure 1 Plot of specific sound attenuation versus ampholyte concentration at 293 K: - - F 3 - - low-frequency limit of sound attenuation, estimated by Equation ( 1 2 ) : - - I I - - e x p e r i m e n t a l values at the high-frequency limit (f=1000 MHZ)
where A and B are frequency-independent constants, c,) is radial frequency, and r 2 is the time of the acoustic relaxation. Parameters A, B and r 2 were calculated by iterational approximation, and the values obtained are listed in Table 1. The existence of the bulk relaxation process could be illustrated by the concentration dependencies of specific sound absorption for the two limiting cases uJr <<1 and ~or >> 1, i.e. at frequencies considerably less than the relaxation frequency of the process and considerably above it, as shown in Fiyure 1. In the first case the limiting values o f ~ f - 2 = A + B were used, which were determined by Equation (12), while for ~ r >>1 we have taken experimental values of sound attenuation at 1000 MHz. It can be seen from Figure 1 that the dependencies could be divided into three regions. In the region of small concentrations (up to 0.100 M, no relaxation processes are observed) both curves practically coincide, while specific absorbance decreases. At medium concentrations (from 0.100 to 0.150 M, acoustical relaxation appears) the specific absorption values reach a minimum and the curves begin to diverge. In the third region (solutions of 0.200 M and greater) the low-frequency curve begins to rise sharply, while the high frequency one remains about constant. The difference between the two curves is due to that part of the total sound absorption which relaxes in the given frequency range (i.e. from about 1 to 1000 MHz). The increasing divergence between the two curves shows, in the most obvious form, the growing contribution of the bulk restructuring processes to the total sound attenuation in the system with increasing surfactant concentration. It turns out that the concentration dependencies of the specific sound absorption could be correlated with the results of viscosity measurements indicating changes in the mechanism of viscous flow of the solutions. Fiyure 2 shows relative viscosities of solutions at different temperatures versus the volume share (4)) of the ampholyte in the system. The volume share was estimated on the basis of density measurements without accounting for the micelle hydration phenomena. It is seen that at concentrations of up to 0.100 M the relative viscosity only slightly depends on concentration and temperature, and is close to the theoretical curve estimated by the
470
Ultrasonics 1994 Vol 32 No 6
(131
The discrepancy between theoretical and experimental curves in this region is most likely caused by our leaving out of consideration the micelle hydration effect. In general, such behaviour signifies that, in dilute solutions, the size of the kinetic units in the system does not vary with temperature and concentration. Most probably the region of small concentrations is characterized by a predominantly spherical form of ampholyte aggregates, which are surrounded by hydration shells of temperature-dependent thickness. The slope of the experimental curves increases sharply with solution concentration, which means that the mechanism of the viscous flow in the system is changing. Obviously, in aqueous solutions of pure surfactant such behaviour could be explained only by restructuring of micellar aggregates and the changing nature of their interactions. In the case of a cationic surfactant belonging to quaternary a m m o n i u m compounds, the most likely reason for the viscosity increase would be formation of rod-like micelles with length, determined by the solution's temperature and concentration 12. It can be seen from Figures 1 and 2 that both concentration dependencies (the specific sound absorption and the relative viscosity) are very similar in appearance. Since viscosity curves indicate to viscous flow processes being determined by micellar interactions, it seems to us not unreasonable to suppose that the slow relaxation process, which is characterized by r 2, is also related to interactions between surfactant aggregates. The intensity of such interactions should increase sharply with concentration, as supported by experimental data (parameter A values in Table 1). It should be noted here that the relaxation times of the slow process, which we have observed directly in our experiments, are several orders of magnitude faster than the characteristic times of the processes found earlier in surfactant solutions by different j u m p methods (pressurejump, temperature-jump, or stopped-flow methods) and which were ascribed to equilibrium processes of micelle monomer exchange 13'14. Additional studies of low
4
.~
3.
3-
2-
~D
1
O
u
i
i
,
,
-4.5 -4 -3.5 -3 -2.5 -2 -1.5 In (volume fraction of ampholyte) Figure 2 Experimental and theoretical plots of relative viscosities versus ampholyte concentration at different temperatures: - - 1 1 - 283 K ; - - A - - 3 0 3 K; + 323 K: E3 353 K; --theoretical curve calculated by Equation (13)
Acoustic spectroscopy of bis-quatemary ammonium ampholyte: V.S. Sperkach et al. frequency sound absorption (in the range from 1 to 10 MHz) have shown that at least in medium-to-high concentration solutions one more slow relaxation process exists with an intrinsic time of the order of 10 -4 to 10- 5 s. As it can be seen from Table 1, in solutions of 0.200 M concentration and greater, the value of the B to ~%f-2 ratio decreases. At first at tow temperatures, and in 0.300 M solution up to 323 K, the B/~tc~f - 2 values are tess than 1. Such behaviour signifies that the molecular mechanism of the acoustic relaxation begins to differ from the one previously described. The process which we observe directly corresponds once more to a joint relaxation of volume and shear viscosities while no indications remain as to the existence of the former high-frequency process. Since relaxation of sound absorption is not complete in the experimental conditions (signified by values of the B parameter being distinct from zero), there should exist some kind of ultra-fast processes with intrinsic frequencies in a still higher range, but our investigations give no clue as to their nature. As for the observed process, it seems reasonable to suppose that it is connected somehow with interactions between rod-like micelles, which intertwine progressively to form a three-dimensional spatial net. Simultaneously with the ampholyte concentration in the solution, the amount of bound water in hydration shells increases. In addition, it is known that bisquaternary a m m o n i u m salts could form in aqueous solutions hydrate compounds. It was reported earlier 15, that salts with tributylammonium headgroups form hydrates with ,-, 100:1 composition, while at low temperatures (below 278K) the crystal hydrates of ~40:1 composition emerge. In our case the molar ratio of components comprised 246:1 for 0,200 M and 154:1 for 0.300 M solutions. So, considering large hydrocarbon radicals of the ampholyte studied, it seems reasonable to assume that in concentrated solutions practically all water should be bonded in hydration shells. In 0.300 M solution, continuous relaxation spectra were obtained below 293 K, where no isolated relaxation processes could be singled out. In our opinion, this means that the formation of the continuous structure is completed in the solution. Most probably the solution structure could be presented as a closely intertwined net of long rod-like micelles (or some kind of integrated spatial aggregate permeated throughout with water molecules). Any rupture or distortion of any bond in such a system should become an irreversible collective process requiring re-ordering of all the neighbouring bonds (that
is, the whole set of bonds in the micro-environment should change).
Conclusions The presented experimental results allowed us to determine the parameters of two relaxation processes in aqueous micellar solutions of bis-quaternary a m m o n i u m ampholyte. The fast process belonging to the picosecond range is related to local restructuring of the weak intermolecular bonds network. A model is offered which allows us to calculate the true values of the thermodynamical potentials of the bond breakage reaction, as well as its transmission coefficient. A second process (intrinsic time ~ 10 - s s) appears in concentrated solutions and, being sensitive to structural dynamic properties of the system, obviously relates to interactions between miceUar aggregates of the ampholyte. Experimental data also testify to the existence of other relaxation processes outside the frequency range studied; that is, both ultra-fast and slow.
References 1 Adamson,A.W. Physical Chemistry of Surfaces Wiley, New York (1982) 2 Mittal,K.L.(Ed} Micellization. Solubilization, and Microemu/sions Plenum Press, New York, London (1977) 3 Denisenko,V.I.and Lopushanski, A.I. Zhurn obshch khimii ( USSR J General Chemistry) (1962) 32 731 (in Russian) 4 Sperkach, V.S., Cholpan, P.F. and Sinilo, V.I. In Fizika zhidkogo sostoyaniya (USSR, Physics of Liquid State) Naukova dumka, Kiev (1979)7 110 (in Russian) 5 6
Sperkach,V.S., Rablchev, E.O. and Gadaibaev, U.Sh. Vestnik MG U (Set Khimiya) (USSR, Bulletin of Moscow State University, Chemistry) (1972) 723 (in Russian) Kachanovskaya, L.D., Makarov, V.G., Ovcharenko, F.D. and Sperkach, V.S. J Surface Sci Technol (1990) 6 241
7
Mason, W.P. (Ed) Properties of gases, liquids and solutions
8
Physical Acoustics vol 2, part A, AcademicPress,New York (1965) Sperkach, V.S. and Shakhparonov, M.I. Zhurn Fiz Khimii (USSR, J Phys Chem) (1981) 55 1732 (in Russian)
9 10 11 12 13 14 15
Shakhparonov,M.I. Mekhanizmybystrykhprotsessovv zidkostyakh (Mechanisms of the Fast processes in Liquids) Vysshaya shkola, Moscow (1980) Shakhparonov, M.I. and Astashenko, E.P. Zhurn Fiz Khimii (USSR, J Phys Chem) (1979) 59 1098 (in Russian) Guth, E. and Simha, R. KoUoid-Z (1936) 74 266 Rehage, H. and Hoffmann, H. Rheol Acta (1982) 21 561 Yasunaga, T., Takeda, K. and Harada, S. J Colloid lnterJace Sci (1973) 42 457 Bennioo,B.C. and Eyrlng, E.M. J Colloid Interface Sci (1970) 32 286 Broadwater,T.L. and Evans, D.F. J Phys Chem (1969) 73 164
Ultrasonics 1994 Vol 32 No 6
471
a n d L.D. K a c h a n o v s k a y a
Institute of Bio-Colloid Chemistry of the Ukrainian Academy of Sciences, 42 Vernadsky Avenue, Kiev 252680, Ukraine
Received 22 September 1993; revised 1 December 1993 Aqueous solutions of surfactants are characterized by the existence of a wide range of relaxation processes. The paper reports on experimental results obtained with aqueous micellar solutions of bis-quaternary ammonium ampholyte by acoustic spectroscopy. Parameters of two relaxation processes lying in the frequency range above 5 MHz were determined, and their probable molecular mechanisms are discussed, The model offered for the description of a fast process (local order restructuring of a network of weak intermolecular bonds) was used to calculate thermodynamical potentials of the reaction and its transmission coefficient.
Keywords: bis-quaternary ammonium ampholyte; micellar solutions; relaxation processes; intermolecular bonds
It is commonly known that surfactant molecules in aqueous solutions form aggregates (micelles) of different shapes and dimensions ,depending on concentration, temperature and other coladitions. Structural transitions between distinctly shaped aggregates are possible under certain conditions and are accompanied by significant changes in physical properties of the solutions. Since surfactant solutions have many practical applications in the different fields of technology, it would be of interest to study structural, physical and thermod.ynamical properties of water-surfactant systems. The investigations of aqueous solutions of tetraalkylammonium compounds and cationic surfactants with trimethylammonium headgroups have previously been carried out by different methods l'z. We have studied aqueous solutions of bis-quaternary ammonium ampholyte (derivative of ethylene-diamine) by ultrasonic relaxation spectroscopy. The surfactant selected possesses high solubility and good surface-active properties, as well as bactericidal and anti-static action. The aim of our investigation was to determine the concentration and temperature relationships of ultrasonic parameters. J
Experimental details The general formula of the bis-quaternary ammonium ampholyte studied is [R-OC(O)CHzN(CH3)2CHzCHzN(CH3) z CHzC(O)O-R] 2 + • 2CIwhere R is a C~o-alkyl radical. The compound was synthesized in the laboratory according to the method 0041 - 624X/ 94 / 06 / 0467-05 © 1994 Butterworth-Heinemann Ltd
of Denisenko and Lopushansky a and was purified by re-crystallization until it was at least 99.5% pure. The solutions were prepared at 293 K by the weight method, with concentrations from 0.010 to 0.300 mole litre- 1. The density of the solutions (p) was determined with a picnometer; the total error amounted to 0.05%. The coefficient of shear viscosity (qs) was measured with a capillary viscosimeter having about 1% accuracy. The experimental technique and the apparatus for ultrasonic measurements have been described elsewhere4'5. The amplitude coefficient of the sound absorption (~) was determined by the pulse method with a variable pathlength in the frequency range extending from 10 to 2800MHz. The measurement error was 2-5% for different frequency values. The velocity of sound (c) was measured at 1 0 M H z with 0.1% accuracy. Additional investigations have shown that dispersion of the sound velocity over the frequency range studied does not exceed 0.1%.
Results and discussion The experimental results obtained are summarized in Table 1. The temperature dependencies of sound absorption, as well as data for some intermediate solution concentrations, are available from the authors. Experimental results have been discussed in part earlier 6. It was established that in relatively dilute solutions (with ampholyte concentrations below 0.100 M) no acoustic relaxation processes were observed in the frequency range studied. The amplitude coefficient of the sound absorption (~) at all temperatures was directly
Ultrasonics 1994 Vol 32 No 6
467
Acoustic spectroscopy of bis-quaternary ammonium ampholyte: V.S. Sperkach Table 1
et al.
Physical and structural relaxation parameters of ampholyte solutions Sound attenuation x l O 15 (m lS2)
Solution
(moll
1)
T
p
(K)
(kgm
2
3
1
3)
qs
c
(mPas)
(ms
4
tlv/tls
1)
A
B
:%.f 2
6
7
8
5
9
rps x 1012
zr × 10 9
(s)
(s)
10
11
Water (q'~ - 0)
283 293 313 333 353
999.6 998.1 992.2 983.2 971.8
1.30 1.02 0.68 0.51 0.40
1447 1483 1529 1550 1554
34 25 16 11 9
11.3 8.2 5.1 3.6 2.9
2.7 2.7 2.8 2.8 2.8
2.5 1.9 1.2 0.9 0.7
0.05 (~b - 0.028)
283 293 313 333 353
1001.2 999.8 993.7 984.3 972.1
1.60 1.23 0.82 0.60 0.47
1450 1486 1532 1550 1552
42 32 19 13 11
13.8 9.9 6.1 4.3 3.4
2.7 3.0 2.8 2.6 3.0
3.1 2.4 1.5 1.0 0.9
0.10 (0 0.056)
283 293 313 333 353
1002.4 1000.9 994.7 985.2 973.2
1.93 1.50 0.99 0.71 0.55
1453 1490 1535 1550 1552
51 12
39 33
16.5 11.9 7.2 5.1 4.0
5.1 3.7 3.3 3.6 3.7
2.9 2.5 1.9 1.5 1.2
6.9 4.5
0.15 (q5 _ 0.084)
283 293 303 313 333
1004.5 1002.5 999.7 995.9 986.5
3.00 2.11 1.57 1.23 0.86
1457 1492 1518 1527 1544
56 34 22 16
54 35 31 24
27,0 16.6 12.0 9.1 6.2
4.1 4.2 4.4 4.5 4.5
3.9 2.6 2.4 1.9 2.1
12.2 9.9 8.4 6.9
0.20 (4) = 0.112)
283 293 303 313 323 333
1005.4 1003.8 1001.1 997.4 992.7 987.4
7.56 4.19 2.60 1.78 1.33 1.06
1467 1493 1513 1527 1537 1541
210 90 52 35 19 16
45 37 26 23 19 18
62.6 33.0 18.3 13.3 9.3 8.8
4.1 4.0 4.3 4.3 4.3 4.3
2.9 2.2 1.9 1.6 1.6
19.9 120 10.5 9.8 8.2 6.5
0.30 (4) - 0.168)
293 303 313 323 333
1006.2 1002.8 998.7 993.9 988.7
43.80 15.97 7.35 4.00 2.57
1504 1516 1527 1530 1535
670 305 115 63 30
66 41 35 30 26
383.0 120.0 54.0 30.0 18.9
1.2 2.4 2.4 2,7 2.7
2.4 2.0
31.8 25.7 19.9 16.9 14.5
-
proportional to the frequency squared. No dispersion of sound absorption was observed. From the comparison with data for pure water it is seen that ampholyte solutions possess excessive sound absorption, which increases sharply with surfactant concentration. This means that the introduction of organic electrolyte molecules results in substantial deformations of the water structure, which in turn enhances different restructuring processes (so-called volume viscosity manifestations). The process of the solution restructuring during acoustic wave propagation takes up finite time, i.e. volume changes are shifted in phase with respect to pressure changes in the system, which causes energy dissipation 7. The value of sound absorption determined by the shear viscosity (the so-called classic absorption) could be calculated by a known equation 7 :z~l.]'' 2 = 2 6 . 3 q ~ p
lc
3
(2)
The resulting values are listed in Table 1. It is seen from Table 1 that in dilute solutions the experimental values of the sound absorption are considerably larger than the calculated values of :tj 2 The relation of ~ f 2 > ~ L [ - 2 signifies that the excessive
468
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sound absorption which we detect in the given frequency range relaxes at still higher frequencies at least in the Gigaherz range. It should be noted here that the general appearance of the temperature dependencies of the above-mentioned parameters for dilute solutions of the ampholyte coincides with the relationships obtained earlier for pure water ~. The absence of the acoustical relaxation manifestations at frequencies below 2.8 G H z means that the intrinsic time of the processes, which determines volume and shear viscosities of the dilute solution, does not exceed 10 ~1 s. This value corresponds in its order of magnitude to the relaxation time of the fastest process observed in liquid water, i.e. the recombination of hydrogen-ions and hydroxyls. For such a reaction, the relaxation time of the volume and shear viscosities should be calculated by the equation ~
I ~c~
(1)
T h e r a t i o o f the c o e f f i c i e n t s o f v o l u m e t o shear v i s c o s i t i e s (~1,,~1~ ~) is defined as
q,,q~ i = 4./3(:z - ~cl)~cl I
25 19 15
rp,
2~.f 2 c
(31
where c o is the velocity of sound at u)z << 1. As we have mentioned, the dispersion of the sound velocity does not exceed 0.1%, so we could assume c o = c. The values of rp, are listed in Table 1. As is seen, the relaxation time increases with increasing solution concentration. This observation seems to indicate that water molecules belonging to hydration shells of the organic electrolyte molecules possess reduced
Acoustic spectroscopy of bis-quaternary ammonium ampholyte: V.S. Sperkach et al. molecular mobility and low velocity of local order restructuring in comparison with the bulk water. As we have mentioned, the acoustical parameters of the dilute solutions turned out to be rather similar to those of water a. By analogy with water, we could assume that the excess sound absorption in the solutions is caused by local order restructuring processes. In such a case, interpretation of the results obtained could be carried out within the framework of a model implying that any arbitrarily chosen macroscopic unit of the solution, taken for consideration in a time period close enough to its relaxation time, should be treated as a dynamic three-dimensional system with molecules connected by weak (such as hydrogen) bonds. The energy fluctuations which emerge due to the thermal motion of the molecules are sufficient to break one or several such bonds. Nevertheless, under thermodynamic equilibrium conditions the number of the broken bonds is equal to the number of the newly formed ones. Now consider a propagation of the sound wave through the solution. The equilibrium is displaced and relaxation processes emerge in the system, resulting in energy dissipation. On the molecular level it means that several bonds (such as O H . . . O, C H . . . O, O H . . . N) are broken, and the parts of the macroscopic system previously connected by these bonds are displaced so that all broken bonds could not restore after the wave has passed. This process is then considered to be a result of a normal reaction, which is a linear combination of all possible monomolecular reactions, accompanied by changes in the total number of weak bonds in the system
viMi , K, , ~. vjMj i
K
i
(4)
j
where the left and right parts of Equation (4) represent a certain volume of the solution before and after the passage of the sound wave, and differ in the number of intermolecular bonds; vi and vj are stoichiometric coefficients; K 1 and K _ 1 are the corresponding rate constants of the forward and backward Reaction (4). If Reaction (4) is not a collective one, we can write the equation for the relaxation time as
z7 1 = Klnl(1/nl + 1/n2) = K 1 + K_ 1
(5)
where n 1 is the number of bonds in the unit volume of the unperturbed solution, and r/2 is a number of bonds broken in the volume as a result of the sound wave passage. If the perturbation is weak enough and a deviation from the equilibrium state is small, we can assume that Kin1 = K_ ln2 . In the case of the acoustical spectroscopy of liquids, when perturbation is induced by
T a b l e 2 Thermodynamical potentials of the reaction of weak intermolecular bonds breakage in water-ampholyte systems Ampholyte concentration (molel 1)
AH* (kJmole 1K 1)
AS'~o p ( J m o l e 1)
AS* (Jmole
Water 0.025 0.050 0.100 0.1 50 0.200
18.6 16.6 14.7 1 5.1 14.9 1 6.5
14.0 5.9 -1.5 -0.2 - 7.5 -4.8
70 63 55 56 49 51
1)
a low-energy sound wave, we can assume nl >> n2, and consequently, K_ 1 >> K r For a consecutive process the limiting stage has the smallest rate constant, so from Equation (5) it follows that K_ 1 = r~-1. According to Shakhparonov 9, the rate constant for a reaction of hydrogen bond breakage could be written in the following form
K_ 1 = 4~zexkRTexp (-AG* ~ \ RT/ h
(6)
where ~cis the transmission coefficient of Reaction (4), ka and h are Boltzmann and Planck constants, and AG* is the free enthalpy, of activation of the bond breaking reaction. After writing the Gibbs free activation energy change in the form A G * = A H * - T A S * , where AH* is an activation enthalpy and AS* is the activation entropy of Reaction (4), we derive AH* = R
c~ln(K_lT -1) c3(T-1)
(7)
So, substituting z~- 1 for K_ 1, and assuming 4~e~- = 1 as a first-order approximation, we can use previously obtained data for the calculation of the apparent values of entropy (AS*pv) and the activation enthalpy of Reaction (4). The resulting thermodynamical parameters are listed in Table 2. Analysis of the data obtained has shown that in diluted ampholyte solutions (up to 0.100 mole litre-1), for the reaction of intermolecular bond breakage, the kinetic compensation effect is observed AH* = a + bAS*pp
(8)
where a and b denote empirical constants. The deviation from the linear correlation in solutions of 0.150 M and more is induced by the appearance of another relaxation process at low temperatures. Because of this, we could not determine AH* values of the first process by Equation (7) as precisely as before. According to Reference 7 R In (4~eK) = - a/b
(9)
so we can determine the true values of entropy and free activation enthalpy by the relationships AS* = ASa*p - R In (4geh-)
(10)
AG* = AGa* p + RTln(4neK)
(11)
The resulting values are also listed in Table 2. We can use Equation (9) to calculate the value of the transmission coefficient, which turned out to be ~" = 2.0 x 10 -5 . This value coincides, to an order of magnitude, with the coefficient values described in the literature for organic liquids characterized by weak intermolecular bonds, such as alcohols 1°. In solutions of 0.100 M concentration and higher, the frequency dependence of the sound absorption appears, which means that the acoustic relaxation process is observed in the system. In concentrated solutions at low temperatures (below 293 K) continuous relaxation spectra were observed, without any distinctly separated processes, and in all the other cases just one isolated process was determined. The sound absorption for such a process is described by the equation v ~f-2 _
A 1 + (09z2)2
+ B
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469
Acoustic spectroscopy of bis-quaternary ammonium ampholyte: V.S. Sperkach et al. G u t h - S i m h a equation for the dilute dispersions of spherical particles 11 qrel = 1 + 2.5~b + 14.1q52 .o=
2
~
1
0
II
I
III
'
o
o 0.05 o'.a o.is 0'.2
o. 5
~unpholyte concentration (M) Figure 1 Plot of specific sound attenuation versus ampholyte concentration at 293 K: - - F 3 - - low-frequency limit of sound attenuation, estimated by Equation ( 1 2 ) : - - I I - - e x p e r i m e n t a l values at the high-frequency limit (f=1000 MHZ)
where A and B are frequency-independent constants, c,) is radial frequency, and r 2 is the time of the acoustic relaxation. Parameters A, B and r 2 were calculated by iterational approximation, and the values obtained are listed in Table 1. The existence of the bulk relaxation process could be illustrated by the concentration dependencies of specific sound absorption for the two limiting cases uJr <<1 and ~or >> 1, i.e. at frequencies considerably less than the relaxation frequency of the process and considerably above it, as shown in Fiyure 1. In the first case the limiting values o f ~ f - 2 = A + B were used, which were determined by Equation (12), while for ~ r >>1 we have taken experimental values of sound attenuation at 1000 MHz. It can be seen from Figure 1 that the dependencies could be divided into three regions. In the region of small concentrations (up to 0.100 M, no relaxation processes are observed) both curves practically coincide, while specific absorbance decreases. At medium concentrations (from 0.100 to 0.150 M, acoustical relaxation appears) the specific absorption values reach a minimum and the curves begin to diverge. In the third region (solutions of 0.200 M and greater) the low-frequency curve begins to rise sharply, while the high frequency one remains about constant. The difference between the two curves is due to that part of the total sound absorption which relaxes in the given frequency range (i.e. from about 1 to 1000 MHz). The increasing divergence between the two curves shows, in the most obvious form, the growing contribution of the bulk restructuring processes to the total sound attenuation in the system with increasing surfactant concentration. It turns out that the concentration dependencies of the specific sound absorption could be correlated with the results of viscosity measurements indicating changes in the mechanism of viscous flow of the solutions. Fiyure 2 shows relative viscosities of solutions at different temperatures versus the volume share (4)) of the ampholyte in the system. The volume share was estimated on the basis of density measurements without accounting for the micelle hydration phenomena. It is seen that at concentrations of up to 0.100 M the relative viscosity only slightly depends on concentration and temperature, and is close to the theoretical curve estimated by the
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The discrepancy between theoretical and experimental curves in this region is most likely caused by our leaving out of consideration the micelle hydration effect. In general, such behaviour signifies that, in dilute solutions, the size of the kinetic units in the system does not vary with temperature and concentration. Most probably the region of small concentrations is characterized by a predominantly spherical form of ampholyte aggregates, which are surrounded by hydration shells of temperature-dependent thickness. The slope of the experimental curves increases sharply with solution concentration, which means that the mechanism of the viscous flow in the system is changing. Obviously, in aqueous solutions of pure surfactant such behaviour could be explained only by restructuring of micellar aggregates and the changing nature of their interactions. In the case of a cationic surfactant belonging to quaternary a m m o n i u m compounds, the most likely reason for the viscosity increase would be formation of rod-like micelles with length, determined by the solution's temperature and concentration 12. It can be seen from Figures 1 and 2 that both concentration dependencies (the specific sound absorption and the relative viscosity) are very similar in appearance. Since viscosity curves indicate to viscous flow processes being determined by micellar interactions, it seems to us not unreasonable to suppose that the slow relaxation process, which is characterized by r 2, is also related to interactions between surfactant aggregates. The intensity of such interactions should increase sharply with concentration, as supported by experimental data (parameter A values in Table 1). It should be noted here that the relaxation times of the slow process, which we have observed directly in our experiments, are several orders of magnitude faster than the characteristic times of the processes found earlier in surfactant solutions by different j u m p methods (pressurejump, temperature-jump, or stopped-flow methods) and which were ascribed to equilibrium processes of micelle monomer exchange 13'14. Additional studies of low
4
.~
3.
3-
2-
~D
1
O
u
i
i
,
,
-4.5 -4 -3.5 -3 -2.5 -2 -1.5 In (volume fraction of ampholyte) Figure 2 Experimental and theoretical plots of relative viscosities versus ampholyte concentration at different temperatures: - - 1 1 - 283 K ; - - A - - 3 0 3 K; + 323 K: E3 353 K; --theoretical curve calculated by Equation (13)
Acoustic spectroscopy of bis-quatemary ammonium ampholyte: V.S. Sperkach et al. frequency sound absorption (in the range from 1 to 10 MHz) have shown that at least in medium-to-high concentration solutions one more slow relaxation process exists with an intrinsic time of the order of 10 -4 to 10- 5 s. As it can be seen from Table 1, in solutions of 0.200 M concentration and greater, the value of the B to ~%f-2 ratio decreases. At first at tow temperatures, and in 0.300 M solution up to 323 K, the B/~tc~f - 2 values are tess than 1. Such behaviour signifies that the molecular mechanism of the acoustic relaxation begins to differ from the one previously described. The process which we observe directly corresponds once more to a joint relaxation of volume and shear viscosities while no indications remain as to the existence of the former high-frequency process. Since relaxation of sound absorption is not complete in the experimental conditions (signified by values of the B parameter being distinct from zero), there should exist some kind of ultra-fast processes with intrinsic frequencies in a still higher range, but our investigations give no clue as to their nature. As for the observed process, it seems reasonable to suppose that it is connected somehow with interactions between rod-like micelles, which intertwine progressively to form a three-dimensional spatial net. Simultaneously with the ampholyte concentration in the solution, the amount of bound water in hydration shells increases. In addition, it is known that bisquaternary a m m o n i u m salts could form in aqueous solutions hydrate compounds. It was reported earlier 15, that salts with tributylammonium headgroups form hydrates with ,-, 100:1 composition, while at low temperatures (below 278K) the crystal hydrates of ~40:1 composition emerge. In our case the molar ratio of components comprised 246:1 for 0,200 M and 154:1 for 0.300 M solutions. So, considering large hydrocarbon radicals of the ampholyte studied, it seems reasonable to assume that in concentrated solutions practically all water should be bonded in hydration shells. In 0.300 M solution, continuous relaxation spectra were obtained below 293 K, where no isolated relaxation processes could be singled out. In our opinion, this means that the formation of the continuous structure is completed in the solution. Most probably the solution structure could be presented as a closely intertwined net of long rod-like micelles (or some kind of integrated spatial aggregate permeated throughout with water molecules). Any rupture or distortion of any bond in such a system should become an irreversible collective process requiring re-ordering of all the neighbouring bonds (that
is, the whole set of bonds in the micro-environment should change).
Conclusions The presented experimental results allowed us to determine the parameters of two relaxation processes in aqueous micellar solutions of bis-quaternary a m m o n i u m ampholyte. The fast process belonging to the picosecond range is related to local restructuring of the weak intermolecular bonds network. A model is offered which allows us to calculate the true values of the thermodynamical potentials of the bond breakage reaction, as well as its transmission coefficient. A second process (intrinsic time ~ 10 - s s) appears in concentrated solutions and, being sensitive to structural dynamic properties of the system, obviously relates to interactions between miceUar aggregates of the ampholyte. Experimental data also testify to the existence of other relaxation processes outside the frequency range studied; that is, both ultra-fast and slow.
References 1 Adamson,A.W. Physical Chemistry of Surfaces Wiley, New York (1982) 2 Mittal,K.L.(Ed} Micellization. Solubilization, and Microemu/sions Plenum Press, New York, London (1977) 3 Denisenko,V.I.and Lopushanski, A.I. Zhurn obshch khimii ( USSR J General Chemistry) (1962) 32 731 (in Russian) 4 Sperkach, V.S., Cholpan, P.F. and Sinilo, V.I. In Fizika zhidkogo sostoyaniya (USSR, Physics of Liquid State) Naukova dumka, Kiev (1979)7 110 (in Russian) 5 6
Sperkach,V.S., Rablchev, E.O. and Gadaibaev, U.Sh. Vestnik MG U (Set Khimiya) (USSR, Bulletin of Moscow State University, Chemistry) (1972) 723 (in Russian) Kachanovskaya, L.D., Makarov, V.G., Ovcharenko, F.D. and Sperkach, V.S. J Surface Sci Technol (1990) 6 241
7
Mason, W.P. (Ed) Properties of gases, liquids and solutions
8
Physical Acoustics vol 2, part A, AcademicPress,New York (1965) Sperkach, V.S. and Shakhparonov, M.I. Zhurn Fiz Khimii (USSR, J Phys Chem) (1981) 55 1732 (in Russian)
9 10 11 12 13 14 15
Shakhparonov,M.I. Mekhanizmybystrykhprotsessovv zidkostyakh (Mechanisms of the Fast processes in Liquids) Vysshaya shkola, Moscow (1980) Shakhparonov, M.I. and Astashenko, E.P. Zhurn Fiz Khimii (USSR, J Phys Chem) (1979) 59 1098 (in Russian) Guth, E. and Simha, R. KoUoid-Z (1936) 74 266 Rehage, H. and Hoffmann, H. Rheol Acta (1982) 21 561 Yasunaga, T., Takeda, K. and Harada, S. J Colloid lnterJace Sci (1973) 42 457 Bennioo,B.C. and Eyrlng, E.M. J Colloid Interface Sci (1970) 32 286 Broadwater,T.L. and Evans, D.F. J Phys Chem (1969) 73 164
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