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Cryometry and excess functions of fullerenols and trismalonates of light fullerenes - C6o(OH)24±2 and C70[=C(COOH)2]3 aqueous solutions
M.Yu. Matuzenko3, D.P. Tyurin3, O. S. Manyakina3, K.N. Semenov1, N.A. Charykov2'3, K. V. Ivanova1, V. A. Keskinov3
1St. Petersburg State University, St. Petersburg, Russia 2St. Petersburg State Electro-technical University (LETI), St. Petersburg, Russia 3St. Petersburg State Technological Institute (Technical University), St. Petersburg, Russia
PACS 61.48.-c DOI 10.17586/2220-8054-2015-6-5-704-714
Cryometry investigations of the C6o(OH)24±2 - H2O and C7o[=C(COOH)2]3 - H2O binary systems were conducted over the 0.1 - 10 g concentration range of fullerenols per 1 dm3 of solutions. The decreases of the temperatures at the onset of H2O - ice crystallization were determined. Excess functions of aqueous solutions - water and fullerenols (trismalonates) activities and activity coefficients and excess Gibbs energy of the solutions were calculated. All solutions demonstrated huge deviations from those of ideal solutions. The last fact, to our opinion, is caused by a very specific - hierarchical type of association of fullerenols (trismalonates) solution components, which was proved by the results of visible light scattering analysis.
Keywords: Cryometry, activities, activity coefficients, fullerenols, trismalonates, water solution. Received: 11 April 2015 Revised: 15 April 2015
1. Introduction
This article is the continuation of a series of articles devoted to the synthesis, identification and physico-chemical properties investigation of nanoclusters, which represented the moderately water soluble derivatives of light fullerenes C60 and C70 [1-14] - poly-hydroxyl fullerenols (fullerenol-d C60(OH)24±2 and malonic ester - trismalonate C70[=C(COOH)2]3). In previous articles' authors have reported on the volume, refraction, electrical, transport properties of these water soluble nanoclusters and their aqueous solutions, also investigations of solubility in water in poly-thermal conditions and in some ternary water-salt systems and complex thermal analysis of nanocluster crystal-hydrates were performed.
2. Reasons for direct excess functions in fullerenols (trismalonates) - H2O solutions determination
We are not aware of any direct experimental data concerning the determination of excess thermodynamic data (primarily activity coefficients) in binary (or more component) solutions of fullerenes or their derivatives in any solutions. This fact may, to our opinion, be explained by the very low solubility of such nanoclusters in the main part of the solvents (see, for example [15-17]). The synthesis of well water soluble nanoclusters (such as: poly-hydroxyl fullerenols C60(OH)n, C70(OH)n; some ethers - for example: trismalonic esters - trismalonate C60[=C(COOH)2]3, C70[=C(COOH)2]3, some adducts with amino-acids (for example arginine C60(C6H12NaN4O2)8H8 or alanine [18]), the solubility of which in water depends on the type
of nanocluster and temperature, may be from tens to hundreds of grams of nanocluster per dm3 of water. This fact makes it possible to determine excess functions of the solution by standard methods, for example, cryometry (described in this article) or by the determination of water activity by isopiestic method. Such determination is, to our opinion, may be very interesting because of the following reasons.
Visible light scattering analysis in light fullerenols (trismalonates) - H2O solutions at room temperature was provided repeatedly (see [1,5,14]). In all cases, one can see the following:
— No monomer molecular nanoclusters (with linear dimension diameter d0 ~ 1.5 — 2.0 nm) were seen in all investigated solutions, even in the dilute solution (C = 0.1 g/dm3).
— The diameters of the first type aggregates (first order clusters of percolation) have similar sizes - some tens of nm di ~ 20 — 80 nm over the whole concentration range.
— The diameters of the second type aggregates (second order clusters of percolation) also have similar sizes - hundreds nm d2 ~ 100 — 400 nm.
— The third type aggregates (third order clusters of percolation) have not been seen at any concentrations except in the most concentrated solution at C > 1 g/dm3, where clusters with extremely huge linear dimension (some microns) are formed: d3 > 1000 nm - the solution 'becomes very heterogeneous' but stable as a colloid system.
— So, to describe these facts in the aggregation process, a stepwise model of particle growth was invoked, in other words, a hierarchical type of association of fullerenols (trismalonates) components in water solution is observed. We consider that monomer spherical molecules form the first type spherical aggregates. Next, the initial spherical associates form the second type spherical associates. Next, the second type spherical associates form the third type spherical associates (the last ones correspond to the colloidal heterogeneous system).
3. The possibility of determining excess functions in fullerenol (trismalonates) - water
solutions
In order to check the possibility of determining the excess function of C60(OH)24±2 -H2O and C70[=C(COOH)2]3 - H2O in the selected concentration range by cryometry method, the following conditions must be met:
— The solubility in the C60(OH)24±2 - H2O and C70[=C(COOH)2]3 - H2O binary systems at ~273.15 K is great enough so that the solution is formally homogeneous, i.e. does not consist of solid crystal hydrates of C60(OH)24±2 or C70[=C(COOH)2]3. Preliminary experiments show that in both cases, the solubilities of both nanoclusters at 273.15 ± 1 K is « 360 g/dm3 for C70[=C(COOH)2]3 and « 210 g/dm3 for Cg0(OH)24±2. So, if we choose the concentration range not more than tens g/dm3 we can be sure that no solid crystal hydrates can co-crystallize with water ice during crystallization of the respective solutions.
— Additionally one must be sure that solutions of the nanoclusters are really homogeneous - do not delaminate and are not colloidal in nature. In this case, only more or less dilute solutions may satisfy these requirements (see lower points 10, 11 in Table 1 were not taken into account).
— The last requirement is that the temperature decrease AT should be more or less significant - hundredth, or even better, tenth of a K. This requirement is easily satisfied.
Table 1. Cryometry data and excess function in the binary solutions ffullerenol-60-d - H2O (marked by *) and trismalonate-C70 - H2O (marked by **) at 273.15 K
Number *Molar fraction of fullerenol-60-d in solution xfullerenol-60-d (rel.un.) *Temperature of water crystallization decrease AT (K) **Molar faction of trismalonate-C70 in solution xfullerenol-70-d (rel. un.) **Temperature of water crystallization decrease AT (K)
1 0.000 0.000 0.000 0.000
2 1.607 ■ 10-6 0.047 1.736 ■ 10-6 0.045
3 3.981 ■ 10-6 0.070 4.430 ■ 10-6 0.064
4 7.933 ■ 10-6 0.099 8.616 ■ 10-6 0.089
5 1.586 ■ 10-5 0.149 1.714 ■ 10-5 0.126
6 3.952 ■ 10-5 0.234 4.275 ■ 10-5 0.183
7 7.905 ■ 10-5 0.350 8.506 ■ 10-5 0.271
8 1.185 ■ 10-4 0.469 1.281 ■ 10-4 0.343
9 1.579 ■ 10-4 0.565 1.710 ■ 10-4 0.410
10 5.130 ■ 10-4 0.785***
11 8.510 ■ 10-4 1.095***
Number *ln aH2o (water activity) (rel. un.) **ln <2H2O (water activity) (rel. un.) *aH2O (water activity) (rel. un.) **«H2O (water activity) (rel. un.)
1 0.000 0.000 1.00000 1.00000
2 -4.236 ■ 10-4 -4.056 ■ 10-4 0.99958 0.99959
3 -6.309 ■ 10-4 -5.775 ■ 10-4 0.99937 0.99942
4 -8.922 ■ 10-4 -8.027 ■ 10-4 0.99911 0.9992
5 -0.00134 -0.00113 0.99866 0.99887
6 -0.00211 -0.00165 0.99789 0.99835
7 -0.00315 -0.00244 0.99685 0.99756
8 -0.00422 -0.00309 0.99579 0.99692
9 -0.00508 -0.00369 0.99493 0.99632
Number *ln YH2O (water activity coefficient) (rel. un.) **ln YH2O (water activity coefficient) (rel. un.) *derivative d ln YH2O **derivative d ln YH2O
dxfullerenol-d (rel. un.) dxtrismalonate-C70 (rel. un.)
1 0.00000 0.00000 -262.6 -230.3
2 -4.22 ■ 10-4 -4.03 ■ 10-4 -174.4 -147.0
3 -6.26 ■ 10-4 -5.73 ■ 10-4 -75.71 -57.99
4 -8.84 ■ 10-4 -7.94 ■ 10-4 -60.303 -45.28
5 -0.00132 -0.00112 -43.51 -28.68
6 -0.00207 -0.00161 -28.42 -18.436
7 -0.00307 -0.00236 -25.71 -15.83
8 -0.0041 -0.00296 -23.47 -13.49
9 -0.00492 -0.00352 -20.82 -13.05
Number *derivative d In Yfullerenol-d dxfullerenol-d (rel. un.) **derivative d In Ytrismalonate-C70 dxtrismalonate-C70 (rel. un.) *ln Yfullerenol-60-d (rel. un.) **ln Ytrismalonate-C70 (rel. un.)
1 - - - -
2 1.08 ■ 108 8.38 ■ 107 2628 2737
3 1.901 ■ 107 1.31 ■ 107 2737 2829
4 7.60 ■ 106 5.24 ■ 107 2780 2860
5 2.74 ■ 106 1.67 ■ 106 2807 2878
6 719101 431233 2835 2896
7 325211 186088 2862 2914
8 198035 105294 2885 2931
9 131834 76302 2906 2947
Number *ln afullerenol-60-d (rel. un.) **ln atrismalonate-C70 (rel. un.) *^&llerenol-60-d (rel. un.) ^trismalonate-C70 (rel. un.)
1 - - - -
2 2614 2724 -195 -205
3 2724 2816 -219 -228
4 2768 2848 -235 -244
5 2795 2867 -252 -261
6 2824 2886 -278 -286
7 2852 2905 -302 -309
8 2875 2922 -318 -326
9 2897 2938 -330 -338
Number *Gex/RT (rel. un.) **Gex/RT (rel. un.) *GmiX/RT (rel. un.) **GmiX/RT (rel. un.)
1 0.00000 0.00000 0.00000 0.00000
2 -0.00186 -0.00178 -0.00186 -0.00178
3 -0.00275 -0.00254 -0.00275 -0.00254
4 -0.00388 -0.00353 -0.00388 -0.00353
5 1.903 ■ 10-5 2.123 ■ 10-5 1.894 ■ 10-5 2.114 ■ 10-5
6 4.844 ■ 10-5 5.381 ■ 10-5 4.825 ■ 10-5 5.360 ■ 10-5
7 9.831 ■ 10-5 1.081 ■ 10-4 9.795 ■ 10-5 1.077 ■ 10-4
8 1.488 ■ 10-4 1.640 ■ 10-4 1.482 ■ 10-4 1.634 ■ 10-4
9 1.999 ■ 10-4 2.203 ■ 10-4 1.993 ■ 10-4 2.196 ■ 10-4
*** - unstable, heterogeneous solution.
4. Cryometry investigation in the Ceo (OH)24±2 - H2O and C70 [=C(COOH)2]3 - H2O binary systems. Main thermodynamic equations
Let us introduce designation:
AF = FS - FL, AT = Tf - T, (1)
where Tf - is the melting point for pure solvent, for water Tf = 273.15 K, T - current temperature (K), AF - molar change of thermodynamic function F, FS - molar function F for the solid phase, FL - molar function F for the liquid phase.
Condition of chemical phase equilibrium liquid (l) - solid (s) for pure solvent - water (w):
= + RT ln aw, (2)
where: , ^u>L - standard chemical potential of the solvent - water, in the solid and liquid phases, correspondingly, aw - water activity in the scale of molar fractions in symmetrical normalization scale. Thus:
- AHW + ACp (T - f + T [ASW - ACp ln (T/T/) ] = RT ln aw, (3)
ln (T/T0f) = ln (T0f - AT/Tf) = ln (1 - AT/T°°) « - AT/T°°, (4)
where: AHW, ASW, ACP - molar enthalpy, entropy and change of isobaric heat capacity of water at the temperature T°°. So:
-AHf [1 - T/Tf + ACp [T - Tf - T ln (t/T°0)] = RT ln aw, (5.1)
-AHf AT/Tf + ACp AT (-1 + T/T°°) = RT ln aw, (5.2)
-AH(wf AT - ACp AT2 (5 3) -7—-x—:— = ln . (5.3)
R T00 - AT T00
Later, we shall use formula (5.3) as a base one for the calculation of the solution's excess functions. In all calculations, we will use symmetrical normalization of the excess functions, as if nanoclusters are very weak electrolytes - practically non-electrolytes (see, for example [4,6,12]). So, we assume that:
«H2O (XH2O = 1) = YH2O (XH2O = 1) = 1, (6.1)
ananocluster (xnanocluster 1) Tnanocluster (xnanocluster 1) -1, (6.2)
where: aj, - activity and activity coefficients of i-th solution component.
Experimental data were obtained with the help of metastatic Beckman thermometer. Data are represented in the Fig. 1 and Table 1. The arrow in the Fig. 1 shows the temperature decrease in the case of an ideal non-electrolyte solution. So, one can see how huge temperature decrease is observed in our cases for water soluble nanocluster solutions.
0,0000 0,0001 0,0002 0,0003 0,0004 0,0005 0,0006 0,0007 0,0008
Molar fraction of nan oc lusters in water solution - x (rel.un.)
tBIDOC llKtâiï
Fig. 1. The decrease of the temperatures of the beginning of the H2O - ice crystallization in fullerenols (trismalonates) - H2O solutions (AT = 273.15 — T)
5. Partial excess functions of water and fullerenols (trismalonates) components in the C6o(OH)24±2 - H2O and C7o[=C(COOH)2]3 - H2O binary systems
The graphics for the dependence ln of water activity (ln aH2O), ln of water activity coefficient (ln YH2O), against molar fraction of fullerenols (trismalonates) in aqueous solutions are represented in Fig. 2, 3 in Table 1. The dependence of the derivative of ln of water (nanocluster)
activity coefficients (d ln YH2o/dXfullerenol-d(trismalonates-C-70)) and
(d ln 7fullerenol-d(tnsmalonate-C-70)/dXfullerenol-d(tnsmalonate-C-70)) in fullerenols (trismalonates) - H2O solutions against molar fraction of fullerenols (trismalonates) in aqueous solutions are also represented in Fig. 4, 5 (curves - approximation, points - experimental data). The approximation is also represented in the Fig. 4, 5. For calculation we used the Gibbs-Duheim equation:
dln ananocluster \ XH2O I d ln aH2O \ (7)
d ln xnanocluster / y xnanocluster \ d ln XH2O / y
The dependence of ln of fullerenols (trismalonates) activity coefficients (ln 7fullerenol-d(tnsmalonate-c-70)) and the ln of fullerenols (trismalonates) activity (ln afuiierenoi-d(tnsmaionate-C-70)) in fullerenols (trismalonates) - H2O solutions against molar fraction of fullerenols (trismalonates) in aqueous solutions are represented in Fig. 6, 7 and Table 1.
6. Excess and Mixing Gibbs energy in the binary systems: C60(OH)24±2 - H2O and C70[=C(COOH)2]3 - H20. Miscibility gap and micro-heterogeneous behavior of the solutions
We have also calculated the dependence of the excess Gibbs energy of the solutions (Gex) in fullerenols (trismalonates) - H2O solutions against the molar fraction of fullerenols (trismalonates) in aqueous solutions (Fig. 8) and the dependence of the Gibbs energy of solution mixing (Gmix) and the miscibility gap in fullerenols (trismalonates) - H2O solutions against molar fraction of fullerenols (trismalonates) (Fig. 9) and also Table 1:
Gex = RT [ln Ynanocluster + XH2O ln Yh2o] , (8)
Fig. 2. The dependence of ln of water activity (lnaH2O) in fullerenols (tris-malonates) - H2O solutions against molar fraction of fullerenols (trismalonates) in aqueous solutions.
Fig. 3. The dependence of ln of water activity coefficients (lnyH2O) in fullerenols (trismalonates) - H2O solutions against molar fraction of fullerenols (trismalonates) in aqueous solutions.
Gmix = RT [xnanocluster ln ananocluster + xH2O ln aH2O] . (9)
One can see the inflection points in the Fig. 8, 9 where the second derivatives:
[5 2Gmix
/d Xnanocluster
JTp and [52 Gex /d ^^anocluster] T,P change signs or derivatives
[5Gmix/5xnanoclusteJ TP and [dGex/5xnanocluster]T,P cross through zero. Geometrically, this means that convexity in the graphics Gex (xnanocluster) and Gmix (xnanocluster) is replaced by the concavity. Additionally, if the behavior of the first function is arbitrarily the sign of the derivative, then [52Gmix/5x2anoclusteJ TP in the concentration range of diffusion stability should be positive. So, we can consider that in the region xnanocluster > 2 ■ 10 5 rel. un., the homogeneous solution exfoliates and becomes micro-heterogeneous. Experiments with light scattering show us that it is concentration region of the transition of the first type aggregates (first order clusters of percolation) with the linear dimensions d « 20 - 80 nm to the second type aggregates (second
Fig. 4. The dependence of the derivative of ln of water activity coefficients (d ln 7H20/dxfullerenol-d(tnsmalonates-C-70)) in fullerenols (trismalonates) - H2O solutions against molar fraction of fullerenols (trismalonates) in aqueous solutions (curves - approximation, points - experimental data).
Fig. 5. The dependence of the derivative of ln of fullerenols (trismalonates)
activity coefficients (d ln 7fullerenol-d(tnsmalonate-C-70)/dxfullerenol-d(tnsmalonate-C-70)) in
fullerenols (trismalonates) - H20 solutions against molar fraction of fullerenols (trismalonates) in aqueous solutions.
Molar fraction of nanodusters in water solution - x (rel.im.)
F ig. 6. The dependence of ln of fullerenols (trismalonates) activity coefficients (ln Yfullerenol-d(trismalonate-c-70)) in fullerenols (trismalonates) - H2O solutions against molar fraction of fullerenols (trismalonates) in aqueous solutions.
0,00000 0,00005 0,00010 0,00015
Molar fraction of nano dusters in water solution - x (rel.un.)
Fig. 7. The dependence of ln of fullerenols (trismalonates) activity (ln afullerenol-d(trismalonate-c-70)) in fullerenols (trismalonates) - H2O solutions against molar fraction of fullerenols (trismalonates) in aqueous solutions.
Fig. 8. The dependence of the excess Gibbs energy of the solutions (Gex) in fullerenols (trismalonates) - H2O solutions against molar fraction of fullerenols (trismalonates) in aqueous solutions
Fig. 9. The dependence of the Gibbs energy mixing of the solutions (Gmix) and the miscibility gap in fullerenols (trismalonates) - H2O solutions against molar fraction of fullerenols (trismalonates) in aqueous solutions
order clusters of percolation) with the linear dimensions d2 ~ 100 — 400 nm. In other words, this is the concentration range where a transition occurs from a nano-heterogeneous system to a micro-heterogeneous one.
Acknowledgements
Investigations were supported by Russian Foundation for Basic Research - RFBR (Project No. 15-08-08438) and with the help of the equipment of Resource Center 'Geomodel' (St.-Petersburg State University).
References
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