Cryometry data and excess thermodynamic functions in the binary system: water soluble bis-adduct of light fullerene C70 with lysine. Assymmetrical thermodynamic model of virtual Gibbs energy decomposition - vd-as Текст научной статьи по специальности «Науки о Земле и смежные экологические науки»

Cryometry data and excess thermodynamic functions in the binary system: water soluble bis-adduct of light fullerene C70 with lysine. Assymmetrical thermodynamic model of virtual gibbs energy decomposition - VD-AS

N. A. Charykov1'5, K.N. Semenov2, V. V. Keskinov1, P. V. Garamova1, D. P. Tyurin1, I. V. Semenyuk1, V. V. Petrenko1, A. V. Kurilenko1, M. Yu. Matuzenko1, N. A. Kulenova3, A. A. Zolotarev1, D. G. Letenko4

1 Saint Petersburg State Technological Institute (Technical University), Moskovsky prospect,

26 Saint Petersburg, 190013, Russia 2 Saint Petersburg State University,7/9 Universitetskaya emb., Saint Petersburg, 199034, Russia 3D. Serikbayev East Kazakhstan state technical university, A. K. Protozanov Street, 69,

Ust-Kamenogorsk city, 070004, The Republic of Kazakhstan 4 Saint Petersburg State University of Architecture and Civil Engineering (SPSUACE), 2-nd Krasnoarmeiskaya St. 4, 190005 Saint Petersburg, Russia 5Saint Petersburg Electrotechnical University "LETI", ul. Professora Popova 5, 197376 Saint Petersburg, Russia [email protected]

PACS 61.48.+c DOI 10.17586/2220-8054-2017-8-3-397-405

The temperature of water-ice crystallization initiation decreases (AT) were determined in the binary water solutions of water soluble derivative of light fullerene C70 with amino-acid lysine at 272.99 - 273.15 K. Partial molar excess functions for H2O were calculated. For the thermodynamic description of our systems, we have elaborated an original semi-empirical model VD-AS (Virial Decomposition Asymmetric Model), based on the virial decomposition of the molar Gibbs energy of the component molar fractions in the solution. With the help of the VD-AS model, partial molar functions of nano-clusters were calculated. Excess and full average Gibbs energies for the solutions and miscibility gaps concentration regions (with the help of diffusional instability equations) were calculated. Thus, the VD-AS model excellently describes pre-delamination or micro-heterogeneous-structure formation in the considered solutions. These calculations were accordingly confirmed by dynamic light scattering data.

Keywords: cryometry, light fullerene C70, lysine, thermodynamic model.

Received: 15 April 2017 Revised: 14 May 2017

1. Introduction

The article is a continuation of the investigations devoted to the synthesis, identification and investigation of physico-chemical properties of water soluble of light fullerene (C60 and C70) derivatives, such as: complex eithers of two-based carbonic acids (malonates, oxalates), poly-hydroxylated forms (fullerenols), amino-acid derivatives (argenine, alanine) some other derivatives [1-23]. In these works, in particular, the physico-chemical properties of aqueous light fullerene derivative solutions, depending on the solutions' concentrations, were investigated: poly-thermal solubility and crystal hydrate compositions; volume properties (density, average and partial component molar volumes); refractive indices, specific and molar refractions; conductivity and pH (apparent dissociation degrees and concentration dissociation constants); associates dimensions and electro-kinetic £ - potentials, etc. The investigation of such fullerenes derivatives is necessary for the following reasons:

First: The application of fullerenes considerably limited by their almost complete incompatibility with water and aqueous solutions, such as, for example: physiological solution, blood, lymph, gastric juice etc. Solubility of light fullerenes, for example, in pure water at 25°C is practically negligible (10-12-10-14 g/dm3 for C60 and C70, correspondingly).

Second: These fullerene derivatives, with amino-acids possess unique anti-oxidant, antibacterial, antiviral and antifungal properties, can absorb different type free radicals, UV photons etc. These facts determine high potential for its application in medicine, pharmacology, cosmetics, food and wine industry etc.

The investigation of the excess thermodynamic functions in such systems (activities, activity coefficients, excess (or mixing) Gibbs energies (enthalpies, entropies) etc.), to the best of our knowledge, until this time, has not been provided, except for two original works [24, 25]. In those articles, in the binary systems with the help of cryometry investigations, the authors determined the decrease in temperature for ice crystallization initiation

(liquidus temperatures), water activities, water activity coefficients, and then, solving numerically the Gibbs-Duhem equation - activities and activity coefficients of fullerene derivatives. No other data concerning the excess function in the considered systems, obtained, for example by the isopiestic method, have been found. Meanwhile, such data may be very scientifically interesting, because these aqueous solutions have very specific and rare consistent hierarchical type of association (see below).

2. Cryometry data in the binary water solutions of water soluble light fullerene derivatives

The temperature of water-ice crystallization initiation decreases (AT) were determined in binary aqueous solutions of water-soluble light fullerene derivative: C70(C6H13N2O2)2 - H2O at 272.99 - 273.15 K. The temperature range corresponds to concentration range X (Molar fraction of C70(C6H13N2O2)2 in the solution) = 0-1.3810-4 rel. un. or C (volume concentration) « 0-10 g/dm3. Such concentrations range for fullerene containing systems is wide enough and corresponds to the solubility of C70(C6H13N2O2)2 in water at 273.15 K. Even at these concentrations, the solutions may lose the diffusive stability, i.e. pre-flake (see below).

Solution concentrations (in molar fractions) vary over a wide range xnano-cluster = 1.1 • 10-6 -1.4 • 10-4 rel.un. The liquidus temperatures were determined with the help of Beckman thermometer with the linear resolution of the device scale AT/Ah « 0.01 K/mm (h - height of Hg capillary raising). Cryometry data AT(xnano-cluster) are shown in Fig. 1 and in Table 1.

Table 1. Cryometry data and excess thermodynamic functions for the bis-lysine adduct of C70 light fullerene - C7o(CeHi3N2O2)2 - H2O binary system at 272.99-273.15 K. Asymmetrical model of excess Gibbs energy decomposition model - VD-AS is used

Molar fraction of C7o(C6Hi3N2O2)2 in the solution XC70(C6H13N 2O2)2 (rel.un.) Ice crystallization initiation temperature decrease AT (K) ln ан2й ln(water activity) (rel.un.) ln YH2O ln (water activity coefficient) (rel.un.) ln YC7o(C6H13N2O2)2 ln (activity coefficient of C70(C6H13N2O2)2 (rel.un.)

0.000 0.000 0.000 0.000 0.000

1.083 10-6 0.005 -5.8610-5 —5.7510-5 3.38

2.16610-6 0.013 —1.4440-4 —1.4210-4 6.65

4.332-10-6 0.020 —2.2240-4 —2.1810-4 12.9

8.6610-6 0.030 —3.3310-4 —3.2510-4 24.3

1.7310-5 0.050 —5.49-10-4 —5.3240-4 42.2

3.46-10-5 0.075 —8.22-10-4 —7.87-10-4 66.0

6.92-10-5 0.11 —0.00122 —0.00116 72.5

1.3810-4 0.16 —0.00178 —0.00164 73.1

Expanded uncertainties are: U(AT) = ±0.002 (dilute solutions) - 0.005 (concentrated solutions) K, Ur(lnaH2o) = 0.5 (concentrated solutions) - 5 (dilute solutions) rel. %, Ur(lnyh2o) = 0.5 (concentrated solutions) - 5 (dilute solutions) rel. % and Ur (ln y"ss ) = 2 (dilute solutions) - 5 (concentrated solutions) rel.% (as the sum result of experimental errors and numerical approximation).

One can see, that all dependencies AT(xnano-cluster) are sharply nonlinear, which prove very high positive deviations of the solutions from ideality for all solutions, even those which are very dilute. In Fig. 1, for comparison, the arrow represents the value ATid for the ideal non-electrolyte solution. We can see the experimental AT exceeds ATid by 1-2 orders of magnitude (for comparable concentrated and dilute solutions, correspondingly). So, one should expect probably gigantic positive deviations of the solution from the ideality in a thermodynamic sense.

Fig. 1. Temperature of water-ice crystallization beginning (liquidus temperature) decrease (AT) against molar fraction concentration in the binary solutions: C7o(C6Hi3N2O2)2 - H2O at 272.99 -273.15 K. Arrow shows AT-function for the ideal non-electrolyte solution

3. Calculation of water excess functions

For calculating the water activity we have used the well-known equation obtained from the equality of chemical H2O potentials in pure solid ice and non-ideal liquid solution [34,35]:

-A#f AT - ACPAT2] / R (Vf - AT) Tf

ln &H2O,

(1)

where AHf = 5990 J/mole, ACP = -38.893 J/mole-K, Tf = 273.15 K heat, temperature of ice fusion and change of heat capacity in the process of ice fusion, correspondingly. Equation (1) was displayed in the symmetrical normalization scale for thermodynamic functions for both solution components:

(2) (3)

f

aR2O (xH2O = 1) = YH2O (xH2O = 1) = 1,

o—cluster (xnano —cluster 1) Ynano-cluster (xnano—cluster 1) 11,

where xi and ai, y - molar fraction, activity and activity coefficient of i-th component.

Calculated data for ln[aH2O(xnano-cluster)] are represented in Fig. 2 and Table. 1.

Additional researchers [24, 25] calculated concentration dependencies ln yh2o, derivatives dln yh2O/dxnano-cluster (numerically). Then, other researchers [34, 35] calculated the dependencies dln Ynano-ciuster/dxnano-ciuster, (according to the classical Gibbs-Duhem differential equation) also numerically and at the end by numerical integration the dependencies ln jnano-cluster (xnano-cluster) were calculated. As a result, as was previously expected, gigantic positive deviations of the solution from ideality for the functions ln ynano-ciuster were obtained ln Ynano-ciuster « «(10° - 101) (see Table 1 and Fig. 4). Naturally, in all likelihood, no existing thermodynamic model can describe such nontrivial behavior of nano-cluster thermodynamic functions.

4. Virial Decomposition Asymmetric Model - VD-AS

For the description of such nontrivial thermodynamic behavior of the considered aqueous solutions, we have elaborated semi-empirical model VD-AS (Virial Decomposition Asymmetric Model), based on the virial decomposition of excess molar Gibbs energy on the solution for the components molar fractions. This technique has often been used for the thermodynamic description of binary and multicomponent systems with different physico-chemical nature, such as: electrolyte solutions [26-29], non-electrolyte (semiconductor) melts [30-33], isovalent

Fig. 2. Logarithm of water activity (ln aH2O) against molar fraction concentration in the binary solutions: C7o(CeHi3N202)2 - H2O at 272.99 - 273.15 K

substitution solid solutions [34-36]. If one takes only one term in the decomposition for the binary system (corresponding to the invariant second virial coefficient), see later equation (4) well-known strictly regular solutions model - RSM, is realized. Under the assumption of temperature dependence for the only virial coefficient, a quasi-regular solution model - QRSM is realized. If one uses third virial coefficients for the decomposition, a sub-regular solution model - SRSM is realized. Finally, when one alsoconsiders the contribution of the electrostatic non-specific interactions (according to Debye-Huckel theory) Pitzer's model in different variants is realized.

So, we assume the following numeration: 1 - is the number of the dissolved component (nano-cluster in our case), 2 - is the number of the solvent (H2O). Let us propose the following expression:

Gex/RT = (m + n2) E E XX ■ Aj = (EE ninJ2 ■ Aj I / (n + «2)i+j-1, (4)

i=i j=i v=i j=i J

where Gex - full molar excess solution Gibbs energy, R = 8.31 J/K, T - temperature (K), ni and Xi - molar number and molar fraction of i-th component, correspondingly, Aij - ij-th virial coefficient in the decomposition of Gex/RT on the component molar numbers. In other words, Aij are naturally identified as divided by RT specific energy of interaction of i particles of the 1-st component and j particles of the 2-nd component. If one takes into account the huge two orders of magnitude) differences in the components' molar masses (1-st are heavy) and its linear dimensions (almost one order - nanoclusters, in our case, are hollow), it is quite clear, that if the upper limit of the summation, according to the 1-st component, is a small natural number (not more than 4-6), the upper limit of the summation, according to the 2-nd component, may be more by one-two orders of magnitude.

Let us calculate excess thermodynamic functions of the components: ln

lnYi = d (Gex/RT) /dni = EE [i - (i + j - 1) Xi] X1-1X2 ■ Aij, (5)

i=i j=i

lnY2 = d (Gex/RT) /dn2 = EE [j - (i + j - 1) X2] XiX^^ ■ Aij. (6)

i=i j=i

In our case, molar fractions of the components are incomparable:

X2 > Xi; X2 > 0.999 « 1, Xi < 1.

(7)

Thus, equations (5), (6) may be simplified:

ln yi « £ iX1-1 £ Aij, (8)

i=1 j=1

ln Y2 « £ (1 - i) Xi £ Aij = £ (1 - i) Xi £ Aij. (9)

i=1 j = 1 i=2 j=1 From the systems (5), (6) and (8), (9) , one can see that, they agree in a thermodynamic sense, i.e. Gibbs-Duhem equation is valid at T, P = const:

X1d ln y1 + X2d ln y2 =0, (10)

or, for example, from the equations (7), (8) we can get identity:

X1 £ i (i - 1) Xi1-2XijdX1 + £ (1 - i) iXi-1XijdX1 = 0. (11)

i=1 i=1 Let us transfer system (8), (9), denoting as Ai summary virial coefficients:

£ Xij =Ai (T), (12)

j=1

so, in our conditions of consideration:

ln Y1 « £ iAiXi-1, (13)

1

ln Y2 «£ (1 - i)AiXi = £(1 - i)AiXj. (14)

li

i=i i=2

v0

One can see that if A1 = 0, then logarithms of the limit activity coefficients - ln yO = limXi^0 ln Yi, correspond to symmetrical method or normalization of the excess thermodynamic functions, namely:

ln y0 = Ai =0, yi (Xi ^ 0) = y0 = 1, (15)

ln y0 = 0, Y2 (Xi ^ 0) = 1. (16)

In our case, for the incomparable, it is more convenient to use the asymmetrical normalization scale (for this, one should only demand the performing of the single condition A1 = 0):

ln y0 = 0, yi (Xi ^ 0)= y0 = 1, (17)

ln y0 = 0, Y2 (Xi ^ 0) = 1, (18)

ln Yaiss « £ iAiXi-i, (19)

i=2

lnYa2ss «£ (1 - i)AiX[. (20)

i=2

This normalization scale will always be used by us as the default.

Let us introduce the function Gmix/RT (divided by RT molar Gibbs energy of mixing), the second isothermal - isobaric concentration derivative of which is equal to the full solution molar Gibbs energy:

Gmix/RT = X1 ln X1 + X2 ln X2 + X1 ln y 1 + X2 ln 72, (21)

d [Gmix/RT] /8X1 =

1/X 1 + 1/X2 - (ln X2 + 1) + £ i2AiX[- 1 + £ (1 - i) Ai [i (i - 1) Xi-2 - (i + 1) X i- 1] , (22)

i= i=2

d2 [Gmix—ass/RT] /dX2 « 1/X i + £i (i - 1) AiX i-2. (23)

tf r ^mix-ass/n^ ICiV 2 _ 1/X 1 + £ i (i - 1) AiX i-2

i=2

in a completely similar manner, we can calculate (divided by RT) first isothermal - isobaric concentration derivative of the chemical potential or logarithm of the activity of the 1-st component - ^ 1 and ln a 1, correspondingly:

1/RT (3^ 1/dX 1) = (d ln a 1/dX1) « 1/X1 + £ i (i - 1) AiXi-2. (24)

i=2

So, the equation of the diffusional (spinodal) stability loss will be the following:

Gm1ix-ass = d2 [Gmix-ass/RT] /dX2 = (d ln a1/dX1) « 1/X1 + £ i (i - 1) AiX^-2 =0. (25)

5. Application of VD-AS model to the description water soluble derivatives of light fullerenes water solutions. Calculation of nanoclusters excess functions. Miscibility gaps

Preliminary calculations show, that the 3-term approximation in the VD-AS - model (i.e. i = 2, 3, 4) is sufficient for more or less successful for the excess thermodynamic functions calculation with the satisfactory accuracy:

ln yTs — 2A2X1 + 3A3X2 + 4A4X?, (26)

ln yTs — -A2X 2 - 2A3X 3 - 3A4X 4. (27)

So, the equation of the diffusional (spinodal) stability loss will be the following:

12A4X 3 + 6A3X2 + 2A2X1 + 1 = 0, (28)

or is explicitly elementarily solved relative to X 1 (according to Cardan formula) cubic equation. All calculated parameters for the VD-AS - model are represented in Table 2.

In all considered binary systems, we calculated the concentration dependencies ln YH2O (see Table 1):

ln Y2 = ln YH2O = ln aH2O - lnXh20 = ln aH2O - ln(1 - Xi), (29)

and from these functions, ln y2(X 1), according to equation (27) and we determined parameters of VD-AS model: A2, A3, A4 (see Table. 2).

Table 2. Parameters of model VD-AS (A2, A3, A4) and concentration boards of diffusion instability regions (Xdiff-instab) in the binary system: C70(C6H 13N202)2 - H20 272.00273.15 K

VD-AS model parameters (rel.un.)

A2 (relun.) A3 (relun.) A4 (relun.) — X diff-instab (rel un )

1.58106 -1.401010 4.1510 13 6.010-5

Formally, the huge values for the summary virial coefficients Ai in general are not surprising, if we remember that, according to the physical sense, they are the sums of the rows, consist of probably thousands terms, responsible for the energies of interactions of a few nano-clusters with a very large number of water molecules.

Then, according to the equation (26), we calculated the concentration dependencies ln y?ss(X 1 )(See Table 1 and Fig. 3). From Fig. 3, one can see that some dependencies ln y"ss (X 1) will cross through the maximum at the values: X1 — 1.510-4 rel. un. (in our case it occurs slightly out of the investigated concentration range). The maximum state may be easily determined from equation (26), solving square equation:

1/2d (ln Y\ss/dX 1) = A2 +3A3X 1 + 6A4X 2 = 0. (30)

Then, according to the equation (28), we determined the boards of diffusional stability loss - Xdiff (see Table 2 and Fig. 4), solving cubic equation:

F = 12A4X 3 + 6A3X 2 + 2A2X1 + 1=0. (31)

As one can see from Table 2, all cubic equations (28) for our considered systems have real positive roots in real concentration ranges, which correspond to the existence of liquid solutions of nano-clusters in water. From this fact, one can conclude that at some concentration range: X diff — 6.0 • 10-5 rel. un. the system begins to display flaking, or perhaps pre-flaking (see later). In Fig. 4, the concentration dependencies of the diffusional instability functions Fdiff-instab = 12A4X 3 + 6A3X2 + 2A2X1 + 1 are represented. From Fig. 4, we see that almost all functions Fdiff-instab(X 1) have intersections with the abscissa axis, which corresponds to diffusional stability loss.

80

0,00000 0,00002 0,00004 0,00006 0,00008 0,00010 0,00012 0,00014 Molar fraction of C (C H NO) in water solutions-X (rel.un.)

70 6 13 2 2 2 C70(C6H13N202)2 v '

Fig. 3. Logarithm of light fullerene water soluble derivative activity coefficient (ln y1) against molar fraction concentration in the binary solutions C7°(CeH13N2O2)2 - H2O at 272.99-273.15 K

Fig. 4. Instability board function F against molar fraction concentration in the binary solutions: C7°(CeH13N2O2)2 - H2O at 272.99-273.15 K

6. Conclusions

(1) The temperature of water-ice crystallization initiation decreases in the binary water solutions of water soluble derivative of light fullerene C70 with the amino-acid lysine were determined at 272.99-273.15 K.

(2) Partial molar excess functions for H20 were calculated.

(3) For the thermodynamic description of our system, we have elaborated original semi-empirical model VD-AS, based on the virial decomposition of molar Gibbs energy of the component molar fractions in the solution.

(4) With the help of VD-AS model partial molar functions of nano-clusters, excess and full average Gibbs energies for the solutions and miscibility gaps concentration regions were calculated.

Acknowledgements

Investigations were supported by Russian Found of Fundamental Investigations - RFFI (Projects NN 15-0808438, 16-08-01206, 15-29-05837) and Fund of Assistance to Development of Small Forms of Enterprises in Scientific-Technical Sphere (Program Start 16-1, Contract No 1549C1/24357).

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