CC BY
7
Maryaskin Yuriy Borisovich, Sc.D., associate professor, Dnepr Chemical-Engineering University, Ukraine E-mail: iryna190856@gmail.com Derman Stanislav Evgenyevich, Engineer, Electrochemist, Metal coating shop foreman
Hamat Group Ltd., Israel E-mail: stanislav.derman@gmail.com
RELATION OF SURFACE-ACTIVE AGENT SOLUTIONS' SURFACE AND VOLUME PROPERTIES
Abstract: An assumption has been made and some data have been provided bearing evidence of the interconnection between volume and surface properties of surface-active agent solutions.
Keywords: adsorption, micelle, surface-active agent, critical micelle formation concentration, surface tension, micelle formation, adsorption capability.
The main colloidal surface-active agent (SAA) properties stipulating the wide practical implementation thereof are the adsorption capacity on the phase interface surfaces and those of micellization in the solution volume.
A significant number of works has been dedicated to the adsorption thermodynamics and micellization [1; 2; 3; 4]. However, in general, the relation between these processes has not been considered in these works.
Further to Shishkovsky adsorption equation, the surface-active agent adsorption goes along with the decreasing of free surface energy on the border of the phase interface.
-Act = ct0 - ct = AoRT ln(l+KC), (l)
whereas, Act - a change of specific free surface energy (surface tension) with the SAA adsorption on the border of the phase interface; ct0, ct - surface tensions of pure (water) solvent and SAA solution, accordingly; Ao - limiting adsorption value; R - gas constant; T - temperature; K - adsorption balance constant; C - SAA concentration in the solution.
It follows from (l) that the solution surface tension decreases as the surface-active agent decreases. This dependency will be observed up to reaching the so-called critical micellization concentration (Ck). When reaching this concentration, the surface tension reaches the constant value, i.e. C is the
1 k
limiting surface-active agent concentration to which the equation (l) will be applicable.
Subsequently, considering that the KCK value >> 1, the equation (l), will make:
-Actk = ct0 - ctk = AjRT lnK+ RT lnCK), (2)
whereas, ctk - SAA solution surface tension when reaching the critical micellization concentration.
At the same time, when reaching CK, the intense micellization [2, l6] is observed in the SAA solution volume. Further to [4, 846; 5, 342], the Gibbs standard energy change during
micellization calculated for one SAA mol is related with the critical micellization concentration by the equation as follows: AG0 . = RT lnC , (3)
mic k v '
whereas, AG0mic - a change of Gibbs standard energy during micellization.
The dependency between the adsorption balance constant and Gibbs standard energy change during the adsorption [5, l46] will be described by the expression as follows: AG0ads = - RT lnK. (4)
whereas, AG0ads - Gibbs energy change during one SAA mol adsorption.
It follows from (2), (3), (4):
-act = A (AG0 - AG0.), (5)
k oox mic ads'1 v '
It is seen from (5) that the surface tension decreasing reached during SAA concentration in the solution equal Ck will be determined by simultaneous progress of two processes: adsorption and micellization. Considering that all the values located in the right side of this equation are constant, the constant value will also get the surface tension value reached during the critical micellization concentration.
For quantitative evaluation of values involved in (5), we used the data provided in [6, 24l-257] pursuant to decreasing of the surface tension in the molecular SAA solutions. C values
K
were defined by the brake of the curve of dependency ct on lnC [5, 339]; further to the graph Act = f(lnC) the limiting adsorption (by the inclination of line) and the adsorption balance constant (by the leg cut off by the line on the axis of the ordinates at lnC = 0) were calculated; further to CK and K values by the equations (3) and (4) AG0mic and AG0ads values were defined.
The received data are provided in (tables l, 2). From these tables it is seen that hydrocarbon chain growth in homologous rows of non-ionic compounds leads to an increase Ao, reduction of surface tension and Gibbs free energy during
adsorption an micellization of one SAA mol. In all cases, when reaching CK, the reduction of AG°ads will be more significant, than AG° K.
mic
Usually, it is assumed that with CK, the adsorption process will be reaching its balance state and only the aggregation of SAA parts in micelle will be possible further on. However, it is known that in some cases, when SAA concentration is increased further on, the spherical micelle destruction will start, and this will be accompanied by decreasing of the surface tension again, i.e. the adsorption and micellization processes mutually make an impact on each other and are in dynamic balance.
Probably, this impact may be explained as follows: When the SAA concentrations in the solution are low, the latter parts easily reach the phase interface borders and they are adsorbed on it. The relation between isobaric - isothermal potential during adsorption and surface-active component chemical potential considering the area of the phase interface border is described by the equation [5, 47]:
Gads = C + Uads ^ (6)
whereas, Gads - Gibbs free surface energy during adsorption, c - solution surface tension; s - phase interface border surface area; uads - surface-active agent chemical potential during adsorption; nads - adsorbed surface-active agent moll quantity.
As the SAA concentration grows, the probability of collision of surface-active agents in the solution volume increases with their following aggregation (micellization) and, accordingly, reaching the solution surface by the SAA parts and their adsorption on the phase interface border will be more difficult. In other words, the adsorption process may be affected by the similar kinetic factor as delivering the SAA to the phase interface border. Probably, under the influence of the above factors, during occurrence of CK there will be the state whereas the rates of adsorption and desorption will become equal. Further on, in spite that the adsorption related to one SAA moll is more advantageous in terms of energy than the micellization, predominantly the second process will be occurring.
According to [7, 145], the micellar structure may be considered as the system composed of many nanoparticles distributed in the liquid environment. Thermodynamic of the system composed ofN equal spherical nanoparticles (micelle) having the average SAA moll number in each micelle equal n is described in [8, 24-26].
In the initial approximation (out of consideration of a possible charge on the surface of micelle, the solution chemical potential change) the Gibbs energy with micellization equals: G = (u n . + W) N. (7)
mic mic mic ' v '
whereas, umic - the chemical potential of surface-active agent during micellization; W - value provided for nanoparts and characterized as a process of interphase border formation (in this case, the micelle interface border - solution).
It is possible to assume that CK is the concentration during which the adsorption processes' free energies and micelliza-tions are equal to one another, i.e. G , = G .. It follows from
ads mic
(6), (7):
cs + u,n, = (u . n . + W) N. (8)
K ads ads mic mic
If we take the phase interface border area as one, then it follows from (8):
c = (u n . + W) N - u ,n , (9)
K mic mic ads ads
Further to [8, 26]:
W = fc°A°, (1°)
Whereas - concentrated phase surface tension (micelle, A° - its surface area, f- constant rate, depending on the surface shape.
It is seen in (9), (1°) that the surface tension value reached during the SAA concentration equal to the critical micellization concentration depends not only on the quantity of adsorbed SAA, but also on the quantity in micelle thereof (and therefore, on its surface area) and on the micelle quantity in the solution volume.
The joint analysis of the above data retrieved at two temperatures will lead to the results which at first glance contradict the adsorption process theoretical concept. For example, it is known that the adsorption - exothermic process accompanied by the heat emission.
AGads = AHads - ^Sad. (ll)
whereas AH, ASads - adsorption enthalpy and entropy change (AG , < AS , < which is possible when AH < i.e. the
v ads 1 ads 1 L ads 1
exothermic process).
For exothermic processes the temperature growth will lead to the reduction of the process balance constant. However, the data provided in Table 3 point that this regularity is observed not in all cases.
Using the received data during processing the adsorption balance constant value reference data pursuant to isobar equation [5, 146] the process enthalpies were calculated (Table 3). The same table provides the micellization heat values (AH ), calculated by Ck values [9, 155-156].
It is seen from the data provided that unlike the adsorption, the micellization will always be accompanied by the heat emission. Even having the same quantity of SAA involved in these processes, this is enough in most cases, so that the total heat effect is less than zero, i. e. with the adsorption the heat emitted as a result of the micellization will be absorbed. Considering that the quantity of SAA involved in micellization is higher than that of involved in adsorption, such an effect will be more significant. Probably the received results are the indirect proof of the above assumption that the adsorption and micellization processes are interconnected and this is reflected in the system thermodynamic characteristics.
It is known that the use of SAA in various technological processes, particularly in the process of cleaning of surfaces from contaminations is related to the adsorption capacity thereof. At the same time, it is noted that SAA with equal adsorption characteristics often have various cleaning effect.
One of the possible reasons of this mismatch is based on the above-mentioned impact of the micellar structures on the adsorption process. The authors intend to dedicate their next work to further examination of this impact.
Table 1. - Values: Ao , A„, AG0 , AG0 d for molecular SAA (T = 298 K)
Formula Aa *103, K ' J/m2 AJ*106 mol/m2 AG0 *103, M ' J/mol AG0 *10-3, ads ' J/mol
1 2 3 4 5
c^occ^oXh -35.2 ,.94 -24.57 -4^8
C,nH,,°(c,H4°XH -41.2 2.66 -28.77 -44.23
C,2H25°(C2H4°)3H -41.5 3J5 -37.4, -50.58
C8H,70(C2H40)6H -3,.5 ,.74 -22.08 -40.23
C,nH„0(C,H40)6H -34.6 2J4 -27.52 -43.69
C„H,50(C,H40)6H -37.2 2.83 -36.32 -49.48
C«H,7°(C,H40)«H -29.7 -20.6, -38.00
CnH,50(C,H40)«H -34.9 2J8 -34.24 -50.25
C,4H,Q°(C,H40)8H -37.7 2.87 -4L77 -54.92
C«H,70(C,H40),nH -28.0 ,.29 -20.56 -42.23
C,nH„0(C,H40),nH -29.9 ,.82 -27.52 -43.98
C„H,50(C,H40),nH -33J ,.82 -30.60 -48.82
C,4H,Q0(C,H40),nH -36.6 2.26 -4L40 -57.59
C«H,7°(C,H40)„H -27.0 ,.37 -,9.44 -39.H
C,nH„0(C,H40)„H -28.8 -27.80 -44.74
C„H,10(C,H4°)„H -32.5 L90 -33.5, -50.6,
C,4H,Q°(C,H40)„H -35.4 2.46 -40.04 -54.43
C»H,V°(C,H40),4H -26.4 -,8.56 -40.36
C,2H250(C,H4°)uH -3lo ,.82 -32.48 -49.54
C,4H290(C2H40),4H -34.3 2.30 -39.44 -54.34
Table 2. - Values: AoK, A„ AG0M AG0ads for molecular SAA (T = 288 K)
Formula Aa *103, K ' J/m2 A„*106, mol/m2 AG0 *103, M ' J/mol AGV *103, ads ' J/mol
1 2 3 4 5
C8H,70(C2H4°)3H -3L4 2.09 -35.90
C,nH„0(C,H40),H -36.3 2.5, -26.84 -43.87
C„H,5°(C,H40),H -37.4 3.76 -34.46 -45.47
C8H,7°(C2H40)6H -27J ,.67 -20.,0 -40.09
C,nH„0(C,H40)6H -30.9 2.09 -25.4, -43.56
C„H,5°(C,H40)6H -32.3 2.5, -32.06 -47.86
C8H,7°(C2H40)8H -29., ,.67 -,8.93 -35.30
C„H,5°(C,H40)8H -3L2 2.09 -3L4, -49.30
C,4H,Q°(C,H40)8H -33.0 3.34 -37.49 -49.95
C8H,70(C,H40),nH -27., ,.25 -H.63 -44.68
C,nH„0(C,H40),nH -27.8 L25 -25J7 -50.26
1 2 3 4 5
C„H,5O(C,H4°),nH -30.0 2.09 -30.62 -44.99
C,4H,Q0(C,H40),nH -32.5 2.09 -37.14 -58.87
C8H,70(C,H40)„H -26.8 1.25 -17.51 -42.29
C,nH„0(C,H40)„H -26.8 1.67 -24.87 -41.88
C„H,5°(C,H40)„H -29.7 2.09 -29.19 -44.51
C,4H,90(C,H40)„H -31.7 2.51 -37.03 -50.26
C»H,70(C2H40),4H -26.6 1.25 -17.30 -39.01
C,2H250(C,H40),4H -29.2 1.67 -29.47 -51.45
C,4H290(C2H40),4H -30.9 2.09 -36.73 -52.17
Table 3. - Values: In K , C , AH . u AH for molecular SAA
equ K ads mic
Formula m lnR equ С *106, к ' mol.shr. D D
288K 298K 288K 298K
1 2 3 4 5 6 7 8
C8H170 (C2H40)mH 3 15 16.6 148 99.5 114.1 -28.4
6 16.76 16.25 226 134.8 -36.4 -36.9
8 14.75 15.35 371 243 42.8 -30.2
10 18.67 17.06 644 248 -114.8 -68.2
12 17.67 15.8 680 389 -133.4 -39.9
14 16.3 16.3 745 556 0 -20.9
C10H210 (C2H40)mH 3 18.33 17.86 13.4 9.0 -33.5 -28.9
6 18.2 17.65 24.5 14.9 -39.2 -35.5
10 21 20.3 27.0 14.9 -49.9 -42.5
12 17.5 18.08 30.5 13.3 41.4 -59.3
C12H250 (C2H40)mH 3 19 20.44 0.558 0.275 102.7 -50.5
6 20 19.98 1.52 0.427 -1.4 -90.7
8 20.6 20.3 2.0 0.988 -21.4 -50.4
10 18.8 19.72 2.27 1.14 65.6 -49.2
12 18.6 20.44 2.60 1.33 131.2 -47.9
14 21.5 20.02 4.47 2.01 -105.5 -57.1
C14H290(C2H40)mH 8 20.87 22.18 0.157 0.0473 93.4 -85.7
10 24.60 23.78 0.182 0.0549 -58.5 -85.6
12 21 21.98 0.191 0.0952 69.9 -49.7
14 21.8 21.95 0.216 0.129 10.7 -36.8
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