- Email: [email protected]
Energetics of phase separation in aqueous solutions of poly(vinyl methyl ether)
Polymer 87 (2016) 283e289
Contents lists available at ScienceDirect
Polymer journal homepage: www.elsevier.com/locate/polymer
Energetics of phase separation in aqueous solutions of poly(vinyl methyl ether) Valerij Y. Grinberg a, *, Tatiana V. Burova a, Natalia V. Grinberg a, Alexander S. Dubovik b, Alexander A. Senin c, Sergey A. Potekhin c, Igor Y. Erukhimovich a a b c
A.N. Nesmeyanov Institute of Organoelement Compounds, Russian Academy of Sciences, Vavilov St. 28, 119991 Moscow, Russian Federation N.M. Emanuel Institute of Biochemical Physics, Russian Academy of Sciences, Kosygin St. 4, 119991 Moscow, Russian Federation Institute of Protein Research, Russian Academy of Sciences, Institutskaya St. 4, Pushchino, Moscow Region 142290, Russian Federation
a r t i c l e i n f o
a b s t r a c t
Article history: Received 14 December 2015 Received in revised form 1 February 2016 Accepted 3 February 2016 Available online 4 February 2016
Phase separation in aqueous solutions of poly(vinyl methyl ether) was first investigated by highsensitivity differential scanning calorimetry at normal and high pressures. Thermograms of the phase separation had two singular points: a binodal point (Tt,1) and a point of the three phases coexistence (Tt,2). At normal pressure the temperature Tt,1 decreased slightly and the temperature Tt,2 was constant (36.8 ± 0.1 С) upon increasing the polymer concentration from 0.01 to 0.25%. The transition enthalpy and heat capacity increment did not depend on the polymer concentration (Dth ¼ 88.0 ± 1.2 J g1; Dtcp ¼ 1.0 ± 0.1 J g1 K1). The calorimetric experiments at high pressures were carried out up to pressure 170 MPa in the range of polymer concentrations 0.1e1.1%. When pressure increased the temperature Tt,1 dropped by 10 C, the temperature Tt,2 increased by 15 C, the total transition enthalpy reduced 1.5 fold and the transition heat capacity increment remained virtually unchanged. These data reveal that the sequential phase transitions, which the diluted aqueous solutions of poly(vinyl methyl ether) undergo upon heating, have different nature. © 2016 Elsevier Ltd. All rights reserved.
Keywords: LCST transition High pressure Differential scanning calorimetry
1. Introduction Amphiphilic polymers are a special class of high-molecular compounds capable of self-organization in aqueous solutions upon heating [1e4]. Examples of such a self-organization are represented by conformational coil-globule transitions, phase or microphase separation, micelle formation and gelation. These phenomena are of great practical interest, especially for solution of various biomedical problems from the directed transport of drugs to controled cell adhesion, enzymatic activity and gene expression [5,6]. Thus, elucidation of principles and mechanisms of the selforganization of aqueous solutions of amphiphilic polymers is an important problem of polymer science. A substantial progress in this direction can be achieved as a result of detailed thermodynamic analysis of conformational and phase transitions of amphiphilic polymers in aqueous medium by obtaining new experimental data in a wide range of temperatures and pressures.
* Corresponding author. E-mail address: [email protected] (V.Y. Grinberg). http://dx.doi.org/10.1016/j.polymer.2016.02.013 0032-3861/© 2016 Elsevier Ltd. All rights reserved.
Such an analysis is possible only on the basis of calorimetric data on energetics of these transitions at various pressures, including the region of very high pressures (of the order of hundreds of MPa). The transition energetics can be evaluated by means of highsensitivity differential scanning calorimetry (HS-DSC) [7e11]. This experimental approach makes it possible to carry out precise calorimetric measurements with microheterogeneous polymer systems at rather low polymer concentrations and heating rates. Under these conditions, the artefacts related to kinetic effects and sedimentation instability of the polymer dispersions are minimized. Therefore, in addition to measurements of the transition temperature and enthalpy HS-DSC provides precise determination of values of the partial heat capacity of polymer before and after the phase transition, i.e. the transition heat capacity increment. These data involve a valuable information on local structure of macromolecules in the coexisting phases. With exact values of the transition temperature, enthalpy and heat capacity increment it is possible to calculate temperature dependences of the transition enthalpy, entropy and free energy. Their analysis enables quantitative comparison of contributions of hydrophobic effect and vander-Waals interactions into driving forces of the transition.
284
V.Y. Grinberg et al. / Polymer 87 (2016) 283e289
Recently, we have shown using PNIPAM as a typical example that precise calorimetric data on energetics of phase separation of aqueous solutions of thermoresponsive polymers can be obtained at high pressures up to about 200 MPa [12]. Simultaneous determination of temperature, enthalpy and width of the phase transition at different pressures gives information on changes in the volume characteristics of a polymer and in the phase diagram of the system. These features provide a basis for more detailed consideration of thermodynamics and mechanism of the phase separation. The manifested potential of HS-DSC at high pressures opens in fact a new direction in physical chemistry of polymers [13]. A goal of this direction is the development of adequate thermodynamic models of self-organization of amphiphilic macromolecules taking into account the transition volume effects. Accumulation of the complementary data on energetics and volume parameters of various types of macromolecular self-organization allows one to track correlations between the structure of a macromolecule in the “organized” state and the change in its volume in the course of selforganization. On the base of these correlations the semiempirical models linking structural, energetic and volume parameters of amphiphilic macromolecules could be developed. In this paper we present results of a first precise calorimetric study of phase separation in diluted aqueous solutions of poly(vinyl methyl ether), PVME (Scheme 1), at normal and high pressures. The characteristic temperatures, enthalpy and heat capacity increment of the phase separation transition were determined as functions of the polymer concentration and pressure. The dependences of the transition temperatures on pressure were approximately analysed in therms of the ClausiuseClayperon equation. This approach allowed determination of signs of the partial volume increments of the polymer associated with sequential phase transitions, which the system undergoes in the course of the phase separation. The information obtained indicates a significant difference in the nature of these transitions.
weight. A polymer concentration in the obtained solutions was controlled by dry residue after drying at 105 C overnight. 2.2. Methods Calorimetric measurements at normal pressure were carried out with a differential adiabatic scanning microcalorimeter DASM-4 (NPO “Biopribor”, Pushchino, Russia) at a heating rate of 1.0 K min1. Experiments at high pressures were performed with the differential scanning microcalorimeter of high pressure SCAL3H (Institute of Protein Research, Pushchino, Russia) also at a heating rate of 1.0 K min1. The measurement part of SCAL-3H is similar to that of the scanning calorimeter SCAL-1 [16]. The measuring and reference cells of the calorimeter are made of glass. A useful volume of the cell is 0.3 mL. The calorimeter allows measurements at a heating rate from 0.1 to 2 K min1 and a pressure up to about 200 MPa in the temperature range 10e100 C. The amount of the sample in the cell was corrected for changes in the density of the solution with increasing pressure. The density of water as a function of temperature and pressure was used for the instrument calibration. Changes in the cell volume due to changes in pressure and temperature were not taken into account because of their negligibility. Measurements of pressure were performed by means of a reference gauge taking into account a ratio of cross-section squares of the inner and outer pistons in the pressure booster. Processing of the thermograms and determination of the phase transition parameters: temperatures Tt,1 and Tt,2, total enthalpy Dth and total heat capacity increment Dtcp, were carried out with a proprietary computer program Nairta 2 (A.N. Nesmeyanov Institute of Organoelement Compounds) using the standard protocols of high-sensitivity differential scanning calorimetry [17]. The cloud points of PVME solutions were visually determined upon heating with a constant rate of 1.0 K min1. 3. Results and discussion
2. Experimental
3.1. Phase separation of aqueous solutions of PVME at normal pressure
2.1. Materials Poly(vinyl methyl ether), PVME, was purchased from “SigmaAldridge” (USA) as 50% aqueous solution and used after an additional purification by the thermoprecipitation procedure [14]. The PVME solution was diluted by water to a concentration of 10%. The solution was heated at a phase separation temperature (45 C) for 3 h. The phases were separated by centrifugation at ~200,000 g for 1 h (Hitachi Centrifuge 70P72). The concentrated phase was diluted to a concentration of 13.7% and used as a stock solution of the polymer. The intrinsic viscosity of the polymer, [h] ¼ 51 ± 2 cm3 g1 was determined in tetrahydrofuran at 25 C. The molecular weight of PVME, Mh ¼ 1.0 105, was calculated by the MarkeHouwink equation [h] ¼ 0.0226 M0.67[15]. Polymer solutions for calorimetric measurements were prepared by dilution of the stock PVME solution (13.7%) with water by
H3C
CH2 CH
n
CH3
O CH3 Scheme 1. Chemical structure of poly(vinyl methyl ether).
The phase behavior of aqueous solutions of PVME is very unusual. The phase diagram of this system has two low critical solution points and probably a line of coexistence of three liquid phases (Fig. 1). When the PVME-Water system with a relatively low polymer content is heated it is possible to anticipate consequent changes in its phase state: at a temperature of crossing the binodal line (Tt,1) and at a temperature of crossing the line of coexistence of three phases (Tt,2). These temperatures correspond to the initial point of the thermogram of phase separation and its maximum, respectively [18]. The known data on calorimetry of phase separation of aqueous solutions of PVME were obtained at normal pressure for rather high polymer concentrations using relatively low-sensitivity instruments [18,19]. It seemed necessary to supplement them with precise data for diluted solutions of the polymer. This study was conducted for different PVME concentrations from 0.1 to 2.5 mg mL1 (0.01e0.25%). The primary calorimetric data were obtained as temperature dependences of apparent partial heat capacity of the polymer. An example of such a dependence is given in Fig. 2. This dependence possesses two singular points: an initial point of the peak (1) as a breakpoint and a maximum point (2). The temperature of the initial point practically coincides with €ferthe cloud point temperature. According to the data of Scha Soenen et al. [18] the temperature of the initial point and the peak maximum temperature were accepted as the binodal temperature Tt,1 and the temperature of coexistence of three phases Tt,2
V.Y. Grinberg et al. / Polymer 87 (2016) 283e289
285
formation of a hydrophobic macromolecular interior of the system as a result of the phase separation. The concentration dependences of the thermodynamic parameters of phase separation of the aqueous solutions of PVME are shown in Fig. 3. It is seen that the temperature Tt,1 demonstrates a
Fig. 1. Schematic presentation of the phase diagram of PVME-Water system in terms of the extended Flory-Huggins theory [18]. Black points represent compositions of the coexisting phases at the given temperature. The dash line and points A, B, C and D display a route of changes in the system state during a HS-DSC experiment at heating from the temperature T0 to the temperature Tend. Points B and C correspond to crossing the binodal at the temperature Tt,1 and the line of coexistence of three phases at the temperature Tt,2, respectively.
Fig. 2. Apparent partial heat capacity of PVME in an aqueous solution under normal pressure. Polymer concentration is 1 mg mL1. The curve displays two singular points: 1, intersection point of the binodal (Tt,1); 2, intersection point of line of the coexistence of three phases; Dtcp < 0, total heat capacity increment of the phase transitions 1 and 2. The temperature Tt,1 coincides with the cloud point temperature of the system. The dash line is a linear approximation of the pre-transition part of the curve.
at the given system composition, respectively. In addition, an important feature of the temperature dependence of partial heat capacity of PVME is the fact that the partial heat capacity after completion of the phase separation is clearly lower than that in the initial homogeneous state of the system. In other words, the total heat capacity increment of the transitions 1 and 2 is negative, Dtcp < 0. This effect is typical of amphiphilic polymers and gels. For example, it has been observed for cross-linked and linear PNIPAM [8,10], poly(N-vinylcaprolactam) [9], and NIPAM-styrene sulfonate copolymers of various composition and structure [11]. A negative value of the heat capacity increment is an evident indication for the
Fig. 3. Thermodynamic parameters of the phase separation of aqueous solutions of PVME under normal pressure: (a) 1, binodal temperature (Tt,1); 2, temperature of the coexistence of three phases (Tt,2 ¼ 36.8 ± 0.1 C); (b) total enthalpy of the phase separation (88.0 ± 1.2 J g1); (c) total heat capacity increment of the phase separation (1.0 ± 0.1 J g1 K1).
286
V.Y. Grinberg et al. / Polymer 87 (2016) 283e289
weak tendency to increase when the polymer concentration decreases in the studied range. On the other hand, the temperature Tt,2 remains unchanged (36.8 ± 0.1 С). The transition enthalpy and heat capacity increment do not depend on the polymer concentration (Dth ¼ 88.0 ± 1.2 J g1; Dtcp¼1.0 ± 0.1 J g1 K1). Note that in respect of the transition parameters PVME far exceeds other thermoresponsive polymers [8e11]. It is well-known that there is a fundamental relation between enthalpies and heat capacity increments of many transitions including protein denaturation, which are associated with transfer of apolar molecules or groups from a parent environment to water [20e22]:
Dt h ¼ Dt cp T TH* þ Dh0
(1)
where T is an arbitrary reference temperature; TH* is the so-called convergence temperature, at which the contribution of hydrophobic hydration to the transition enthalpy vanishes; and term Dth0 takes into account the contribution of van der Waals interactions or hydrogen bonds to the transition enthalpy. There are different estimates of the convergence temperature that are rather close to each other. Nevertheless, a value of this temperature, TH* ¼ 110 C, determined from calorimetric data for small globular proteins by Privalov and Khechinashvili [20] seems to be preferable. We used Eq (1) for correlation of the data for PVME and other thermoresponsive polymers previously studied [8e11] at a temperature T¼ 34.7 C, which is an averaging of the transition temperatures of the polymers under consideration. As shown in Fig. 4 there is a linear correlation between the transition enthalpy and heat capacity increment for thermoresponsive polymers of different composition and structure. From the slope of the correlation line it is followed that the convergence temperature TH* is 111 C. Our estimate of TH* coincides perfectly with the convergence temperature determined by Privalov and Khechinashvili for a number of globular proteins [20]. This fact seems to be of general significance for understanding origin and main driving forces of the thermoresponsive polymer self-organization. It suggests a deep
Fig. 4. Correlation between the LCST transition parameters of some thermoresponsive polymers according to Eq. (1): PVME (1), PNIPAM (2) [11], PNIPAM (3) [10], NIPAM gel (4) [8], poly(N-vinylcaprolactam) (5) [9], NIPAM-styrene sulfonate (2%) copolymer (6) [11], NIPAM-styrene sulfonate (20%) copolymer (7) [11], N-vinyicaprolactam-MAAc (12%) copolymer (8) [9], N-vinyicaprolactam-MAAc (18%) copolymer (9) [9]. The slope of the correlation line indicates that the convergence temperature TH* is 111 C. Correlation coefficient is 0.945.
similarity of hydrophobic hydration of polymer chains composed of different hydrophobic groups. Contribution of hydrophobic hydration into the transition energetics is apparently not influenced by hydrophilic part of a thermoresponsive macromolecule. 3.2. Phase separation of aqueous solutions of PVME at high pressures This research was carried out in a pressure range up to 170 MPa at different concentrations of the polymer from 1 to 11 mg mL1 (0.1e1.1%). Typical excess heat capacity functions of phase separation at various pressures are compared in Fig. 5. The singular points (crossing points with the binodal and the line of coexistence of three phases) mentioned above are clearly seen on all curves. When pressure increases, the resolution of these points becomes more and more descriptive while a heat response from the change in phase state of the system decreases rapidly. Fig. 6 illustrates the pressure effects on the calorimetric parameters of phase separation of aqueous PVME solutions. The binodal temperature Tt,1 decreases by 10 С, the three-phases coexistence temperature Tt,2 increases by 15 C and the total transition enthalpy is reduced 1.5 fold upon increase in pressure. Significantly, the pressure dependences of the calorimetric parameters obtained at different polymer concentrations coincide within the experimental errors. A strict interpretation of dependences of the phase separation
Fig. 5. Excess heat capacity functions of phase separation of aqueous solutions of PVME under different pressures, MPa: 0.0981 (a), 24.2 (b), 47.0 (c), 69.7 (d). The curves are arbitrarily shifted along the ordinate axis to avoid overlap. The singular points of curves: 1, intersection point of the binodal; 2, intersection point of the line of coexistence of three phases. Polymer concentration is of 4.26 mg mL1.
V.Y. Grinberg et al. / Polymer 87 (2016) 283e289
vln Tt Dt v y Dt h vp
287
(2)
where Tt is the characteristic transition temperature; Dtv is the transition change in the partial volume of polymer; Dth is the transition enthalpy. In our case there are two consequent phase transitions with the characteristic temperatures Tt,1 and Tt,2. For convenience of consideration, their pressure dependences are given in the semilog form: ln Tt,1 ¼ f(p) and ln Tt,2 ¼ f(p), in Fig. 7. We can write the corresponding ClausiuseClayperon equation for each of them:
vln Tt;1 Dt v1 y vp Dt h1
(3)
vln Tt;2 Dt v2 y vp Dt h2
(4)
where Dtv1 and Dtv2 are the changes in the partial volume of polymer as result of the crossing of the binodal and the line of coexistence of three phases (the phase transitions 1 and 2, respectively); Dth1 andDth2 are the enthalpies of these transitions. The obtained calorimetric data do not allow one to estimate the
Fig. 6. Calorimetric parameters of phase separation of aqueous solutions of PVME vs. pressure: (a) the temperature of the binodal; (b) the temperature of coexistence of three phases; (c) total transition enthalpy. Polymer concentration, mg mL1: 1.0 (1), 2.0 (2), 4.3 (3) and 10.6 (4).
temperature of solutions (in particular, of aqueous solutions of polymers) on pressure is a specific theoretical problem. However we believe that for a qualitative consideration of the phenomenon it is possible to accept this dependence in the form of the ClausiuseClayperon equation [23]:
Fig. 7. Semi-log plots of the characteristic temperatures of the phase diagram of aqueous solutions of PVME on pressure: (a) the binodal temperature; (b) the temperature of coexistence of three phases. Polymer concentration, mg mL1: 1.0 (1), 2.0 (2), 4.3 (3), 10.6 (4).
288
V.Y. Grinberg et al. / Polymer 87 (2016) 283e289
enthalpies Dth1 and Dth2 because of strong overlapping the transitions 1 and 2. Nevertheless, it is quite evident that both enthalpies are positive, that is, Dth1 > 0 и Dth2 > 0. It follows that a slope of the pressure dependence of logarithm of the characteristic temperature will be determined by a sign of the transition increment of partial volume of polymer. The slope of the dependence ln Tt,1 ¼ f(p) is negative. Consequently, Dtv1 < 0. In contrast, the slope of the dependence ln Tt,2 ¼ f(p) is positive and correspondingly Dtv2 > 0. Thus the increments of partial volume of polymer associated with the consequent phase transitions, which the diluted aqueous solutions of PVME undergo upon heating, have opposite signs. This difference seems to be of a principal importance. It suggests that these phase transitions are of different nature. It is still difficult to say about a nature of the first transition. In contrast, the nature of the second transition is in general clear, since the positive partial volume increment of polymer is typical of the transitions accompanied by a change in accessibility of apolar residues of the polymer to water molecules, e.g. for denaturation of globular proteins [24]. It should be noted that the theoretical models elaborated for description of the phase behaviour of aqueous solutions of PVME [18,19] consider the consequent transitions in this system in framework of a single equation of state. So they do not distinguish these transitions by their nature. Our data emphasizing the differences in the nature of the transitions indicate a need of elaboration of new theoretical approaches for description of very unusual properties of PVME. The transition heat capacity increment is one of the key thermodynamic parameters helping to understand a nature of the transition [25]. Therefore it was of importance to determine the heat capacity increment of the phase separation of aqueous solutions of PVME under different pressures. We could performed such measurements only at a relatively high polymer concentration of 10.6 mg mL1 (~1.1%) because of some technical problems. Such a concentration allowed determination of the transition heat capacity increment with a good precision but without simultaneous determination of the transition enthalpy because of cutting the top of the heat capacity peak due to the saturation of the thermal sensor of the calorimeter at excessively high heat absorption of the sample. The temperature dependence of the apparent partial heat capacity of PVME at pressure 23.5 MPa is presented in Fig. 8a. This figure underlines a complex calorimetric profile of the phase separation: the presence of the first singular point associated with the transition of the system through the binodal and a clear decrease in the partial heat capacity of the polymer as a result of phase separation. Fig. 8b shows that the transition heat capacity increment remains unchanged in the studied pressure interval, Dtcp ¼ 1.2 ± 0.1 J g1 K1. This value agrees well with the result of determination of the heat capacity increment at normal pressure and low polymer concentrations.
Fig. 8. (a) Apparent partial heat capacity of PVME in an aqueous solution under pressure 23.5 MPa. Polymer concentration is 10.6 mg mL1. The binodal point is shown by an empty point. A top of the curve is cut off as a result of saturation of the thermal sensor of the calorimeter. (b) Total LCST transition heat capacity increment of PVME vs. pressure. Its average value is 1.2 ± 0.1 J g1 K1.
depend on the polymer concentration and pressure. A linear correlation between the enthalpies and heat capacity increments of the LCST transitions of a number of thermoresponsive polymers including poly(vinyl methyl ether) is found. It shows that the convergence temperature TH* , at which the contribution of hydrophobic hydration to energetics of the LCST transitions vanishes, is close to the convergence temperature of globular proteins (TH* ¼ 110 С).
4. Conclusion The diluted aqueous solutions of poly(vinyl methyl ether) undergo the consequent phase transitions upon heating. The first transition temperature decreases with increasing the polymer concentration and pressure. The second transition temperature does not depend on the polymer concentration but increases with increasing the pressure. The first transition is accompanied by the decrease and the second one - by the increase in the partial specific volume of the polymer. This principal difference seems to reveal that natures of these transitions differ drastically. The total enthalpy of both transitions does not depend on the polymer concentration and decreases with increasing pressure. The total heat capacity increment of the transitions is negative. It does not
Acknowledgement The financial support from the Russian Foundation for Basic Research (project 13-03-00574) is greatly appreciated. References [1] [2] [3] [4] [5] [6]
H.G. Schild, Prog. Polym. Sci. 17 (2) (1992) 163e249. P. Alexandridis, T.A. Hatton, Colloids Surfaces A 96 (1e2) (1995) 1e46. V.O. Aseyev, H. Tenhu, F.M. Winnik, Adv. Polym. Sci. 196 (2006) 1e85. V. Aseyev, H. Tenhu, F.M. Winnik, Adv. Polym. Sci. 242 (2011) 29e89. E.S. Gil, S.M. Hudson, Prog. Polym. Sci. 29 (12) (2004) 1173e1222. C.D.H. Alarcon, S. Pennadam, C. Alexander, Chem. Soc. Rev. 34 (3) (2005) 276e285.
V.Y. Grinberg et al. / Polymer 87 (2016) 283e289 [7] N.V. Grinberg, A.S. Dubovik, V.Y. Grinberg, D.V. Kuznetsov, E.E. Makhaeva, A.Y. Grosberg, T. Tanaka, Macromolecules 32 (5) (1999) 1471e1475. [8] V.Y. Grinberg, A.S. Dubovik, D.V. Kuznetsov, N.V. Grinberg, A.Y. Grosberg, T. Tanaka, Macromolecules 33 (23) (2000) 8685e8692. [9] A.S. Dubovik, E.E. Makhaeva, V.Y. Grinberg, A.R. Khokhlov, Macromol. Chem. Phys. 206 (9) (2005) 915e928. [10] A.S. Dubovik, N.V. Grinberg, V.Y. Grinberg, Polym. Sci. Ser. A 52 (6) (2010) 565e573. [11] V.Y. Grinberg, T.V. Burova, N.V. Grinberg, A.S. Dubovik, I.G. Plaschina, T.V. Laptinskaya, Y. Xiong, P. Yao, A.R. Khokhlov, Macromol. Chem. Phys. 216 (24) (2015) 2344e2355. [12] V.Y. Grinberg, A.A. Senin, N.V. Grinberg, T.V. Burova, A.S. Dubovik, S.A. Potekhin, I.Y. Erukhimovich, Polymer 64 (2015) 14e18. [13] S.A. Potekhin, Polym. Sci. Ser. C 54 (1) (2012) 108e115. [14] E. Loozen, E. Nies, K. Heremans, H. Berghmans, J. Phys. Chem. B 110 (15) (2006) 7793e7802.
289
[15] C. Querner, T. Schmidt, K.F. Arndt, Langmuir 20 (7) (2004) 2883e2889. [16] A.A. Senin, S.A. Potekhin, E.I. Tiktopulo, V.V. Filomonov, J. Therm, Anal. Calorim. 62 (1) (2000) 153e160. [17] P.L. Privalov, S.A. Potekhin, Methods Enzymol. 131 (1986) 4e51. €fer-Soenen, R. Moerkerke, H. Berghmans, R. Koningsveld, K. Dusek, [18] H. Scha K. Solc, Macromolecules 30 (3) (1997) 410e416. [19] K. Van Durme, G. Van Assche, E. Nies, B. Van Mele, J. Phys, Chem. B 111 (6) (2007) 1288e1295. [20] P.L. Privalov, N.N. Khechinashvili, J. Mol. Biol. 86 (3) (1974) 665e684. [21] R.L. Baldwin, N. Muller, P. Natl, Acad. Sci. U. S. A. 89 (15) (1992) 7110e7113. [22] K.P. Murphy, E. Freire, Adv. Protein Chem. 43 (1992) 313e361. [23] I. Prigogine, R. Defay, Chemical Thermodynamics, Longmans Green Co., London-N.Y.-Toronto, 1954. [24] M. Gross, R. Jaenicke, Eur. J. Biochem. 221 (2) (1994) 617e630. [25] G.I. Makhatadze, P.L. Privalov, Adv. Protein Chem. 47 (1995) 307e425.
Contents lists available at ScienceDirect
Polymer journal homepage: www.elsevier.com/locate/polymer
Energetics of phase separation in aqueous solutions of poly(vinyl methyl ether) Valerij Y. Grinberg a, *, Tatiana V. Burova a, Natalia V. Grinberg a, Alexander S. Dubovik b, Alexander A. Senin c, Sergey A. Potekhin c, Igor Y. Erukhimovich a a b c
A.N. Nesmeyanov Institute of Organoelement Compounds, Russian Academy of Sciences, Vavilov St. 28, 119991 Moscow, Russian Federation N.M. Emanuel Institute of Biochemical Physics, Russian Academy of Sciences, Kosygin St. 4, 119991 Moscow, Russian Federation Institute of Protein Research, Russian Academy of Sciences, Institutskaya St. 4, Pushchino, Moscow Region 142290, Russian Federation
a r t i c l e i n f o
a b s t r a c t
Article history: Received 14 December 2015 Received in revised form 1 February 2016 Accepted 3 February 2016 Available online 4 February 2016
Phase separation in aqueous solutions of poly(vinyl methyl ether) was first investigated by highsensitivity differential scanning calorimetry at normal and high pressures. Thermograms of the phase separation had two singular points: a binodal point (Tt,1) and a point of the three phases coexistence (Tt,2). At normal pressure the temperature Tt,1 decreased slightly and the temperature Tt,2 was constant (36.8 ± 0.1 С) upon increasing the polymer concentration from 0.01 to 0.25%. The transition enthalpy and heat capacity increment did not depend on the polymer concentration (Dth ¼ 88.0 ± 1.2 J g1; Dtcp ¼ 1.0 ± 0.1 J g1 K1). The calorimetric experiments at high pressures were carried out up to pressure 170 MPa in the range of polymer concentrations 0.1e1.1%. When pressure increased the temperature Tt,1 dropped by 10 C, the temperature Tt,2 increased by 15 C, the total transition enthalpy reduced 1.5 fold and the transition heat capacity increment remained virtually unchanged. These data reveal that the sequential phase transitions, which the diluted aqueous solutions of poly(vinyl methyl ether) undergo upon heating, have different nature. © 2016 Elsevier Ltd. All rights reserved.
Keywords: LCST transition High pressure Differential scanning calorimetry
1. Introduction Amphiphilic polymers are a special class of high-molecular compounds capable of self-organization in aqueous solutions upon heating [1e4]. Examples of such a self-organization are represented by conformational coil-globule transitions, phase or microphase separation, micelle formation and gelation. These phenomena are of great practical interest, especially for solution of various biomedical problems from the directed transport of drugs to controled cell adhesion, enzymatic activity and gene expression [5,6]. Thus, elucidation of principles and mechanisms of the selforganization of aqueous solutions of amphiphilic polymers is an important problem of polymer science. A substantial progress in this direction can be achieved as a result of detailed thermodynamic analysis of conformational and phase transitions of amphiphilic polymers in aqueous medium by obtaining new experimental data in a wide range of temperatures and pressures.
* Corresponding author. E-mail address: [email protected] (V.Y. Grinberg). http://dx.doi.org/10.1016/j.polymer.2016.02.013 0032-3861/© 2016 Elsevier Ltd. All rights reserved.
Such an analysis is possible only on the basis of calorimetric data on energetics of these transitions at various pressures, including the region of very high pressures (of the order of hundreds of MPa). The transition energetics can be evaluated by means of highsensitivity differential scanning calorimetry (HS-DSC) [7e11]. This experimental approach makes it possible to carry out precise calorimetric measurements with microheterogeneous polymer systems at rather low polymer concentrations and heating rates. Under these conditions, the artefacts related to kinetic effects and sedimentation instability of the polymer dispersions are minimized. Therefore, in addition to measurements of the transition temperature and enthalpy HS-DSC provides precise determination of values of the partial heat capacity of polymer before and after the phase transition, i.e. the transition heat capacity increment. These data involve a valuable information on local structure of macromolecules in the coexisting phases. With exact values of the transition temperature, enthalpy and heat capacity increment it is possible to calculate temperature dependences of the transition enthalpy, entropy and free energy. Their analysis enables quantitative comparison of contributions of hydrophobic effect and vander-Waals interactions into driving forces of the transition.
284
V.Y. Grinberg et al. / Polymer 87 (2016) 283e289
Recently, we have shown using PNIPAM as a typical example that precise calorimetric data on energetics of phase separation of aqueous solutions of thermoresponsive polymers can be obtained at high pressures up to about 200 MPa [12]. Simultaneous determination of temperature, enthalpy and width of the phase transition at different pressures gives information on changes in the volume characteristics of a polymer and in the phase diagram of the system. These features provide a basis for more detailed consideration of thermodynamics and mechanism of the phase separation. The manifested potential of HS-DSC at high pressures opens in fact a new direction in physical chemistry of polymers [13]. A goal of this direction is the development of adequate thermodynamic models of self-organization of amphiphilic macromolecules taking into account the transition volume effects. Accumulation of the complementary data on energetics and volume parameters of various types of macromolecular self-organization allows one to track correlations between the structure of a macromolecule in the “organized” state and the change in its volume in the course of selforganization. On the base of these correlations the semiempirical models linking structural, energetic and volume parameters of amphiphilic macromolecules could be developed. In this paper we present results of a first precise calorimetric study of phase separation in diluted aqueous solutions of poly(vinyl methyl ether), PVME (Scheme 1), at normal and high pressures. The characteristic temperatures, enthalpy and heat capacity increment of the phase separation transition were determined as functions of the polymer concentration and pressure. The dependences of the transition temperatures on pressure were approximately analysed in therms of the ClausiuseClayperon equation. This approach allowed determination of signs of the partial volume increments of the polymer associated with sequential phase transitions, which the system undergoes in the course of the phase separation. The information obtained indicates a significant difference in the nature of these transitions.
weight. A polymer concentration in the obtained solutions was controlled by dry residue after drying at 105 C overnight. 2.2. Methods Calorimetric measurements at normal pressure were carried out with a differential adiabatic scanning microcalorimeter DASM-4 (NPO “Biopribor”, Pushchino, Russia) at a heating rate of 1.0 K min1. Experiments at high pressures were performed with the differential scanning microcalorimeter of high pressure SCAL3H (Institute of Protein Research, Pushchino, Russia) also at a heating rate of 1.0 K min1. The measurement part of SCAL-3H is similar to that of the scanning calorimeter SCAL-1 [16]. The measuring and reference cells of the calorimeter are made of glass. A useful volume of the cell is 0.3 mL. The calorimeter allows measurements at a heating rate from 0.1 to 2 K min1 and a pressure up to about 200 MPa in the temperature range 10e100 C. The amount of the sample in the cell was corrected for changes in the density of the solution with increasing pressure. The density of water as a function of temperature and pressure was used for the instrument calibration. Changes in the cell volume due to changes in pressure and temperature were not taken into account because of their negligibility. Measurements of pressure were performed by means of a reference gauge taking into account a ratio of cross-section squares of the inner and outer pistons in the pressure booster. Processing of the thermograms and determination of the phase transition parameters: temperatures Tt,1 and Tt,2, total enthalpy Dth and total heat capacity increment Dtcp, were carried out with a proprietary computer program Nairta 2 (A.N. Nesmeyanov Institute of Organoelement Compounds) using the standard protocols of high-sensitivity differential scanning calorimetry [17]. The cloud points of PVME solutions were visually determined upon heating with a constant rate of 1.0 K min1. 3. Results and discussion
2. Experimental
3.1. Phase separation of aqueous solutions of PVME at normal pressure
2.1. Materials Poly(vinyl methyl ether), PVME, was purchased from “SigmaAldridge” (USA) as 50% aqueous solution and used after an additional purification by the thermoprecipitation procedure [14]. The PVME solution was diluted by water to a concentration of 10%. The solution was heated at a phase separation temperature (45 C) for 3 h. The phases were separated by centrifugation at ~200,000 g for 1 h (Hitachi Centrifuge 70P72). The concentrated phase was diluted to a concentration of 13.7% and used as a stock solution of the polymer. The intrinsic viscosity of the polymer, [h] ¼ 51 ± 2 cm3 g1 was determined in tetrahydrofuran at 25 C. The molecular weight of PVME, Mh ¼ 1.0 105, was calculated by the MarkeHouwink equation [h] ¼ 0.0226 M0.67[15]. Polymer solutions for calorimetric measurements were prepared by dilution of the stock PVME solution (13.7%) with water by
H3C
CH2 CH
n
CH3
O CH3 Scheme 1. Chemical structure of poly(vinyl methyl ether).
The phase behavior of aqueous solutions of PVME is very unusual. The phase diagram of this system has two low critical solution points and probably a line of coexistence of three liquid phases (Fig. 1). When the PVME-Water system with a relatively low polymer content is heated it is possible to anticipate consequent changes in its phase state: at a temperature of crossing the binodal line (Tt,1) and at a temperature of crossing the line of coexistence of three phases (Tt,2). These temperatures correspond to the initial point of the thermogram of phase separation and its maximum, respectively [18]. The known data on calorimetry of phase separation of aqueous solutions of PVME were obtained at normal pressure for rather high polymer concentrations using relatively low-sensitivity instruments [18,19]. It seemed necessary to supplement them with precise data for diluted solutions of the polymer. This study was conducted for different PVME concentrations from 0.1 to 2.5 mg mL1 (0.01e0.25%). The primary calorimetric data were obtained as temperature dependences of apparent partial heat capacity of the polymer. An example of such a dependence is given in Fig. 2. This dependence possesses two singular points: an initial point of the peak (1) as a breakpoint and a maximum point (2). The temperature of the initial point practically coincides with €ferthe cloud point temperature. According to the data of Scha Soenen et al. [18] the temperature of the initial point and the peak maximum temperature were accepted as the binodal temperature Tt,1 and the temperature of coexistence of three phases Tt,2
V.Y. Grinberg et al. / Polymer 87 (2016) 283e289
285
formation of a hydrophobic macromolecular interior of the system as a result of the phase separation. The concentration dependences of the thermodynamic parameters of phase separation of the aqueous solutions of PVME are shown in Fig. 3. It is seen that the temperature Tt,1 demonstrates a
Fig. 1. Schematic presentation of the phase diagram of PVME-Water system in terms of the extended Flory-Huggins theory [18]. Black points represent compositions of the coexisting phases at the given temperature. The dash line and points A, B, C and D display a route of changes in the system state during a HS-DSC experiment at heating from the temperature T0 to the temperature Tend. Points B and C correspond to crossing the binodal at the temperature Tt,1 and the line of coexistence of three phases at the temperature Tt,2, respectively.
Fig. 2. Apparent partial heat capacity of PVME in an aqueous solution under normal pressure. Polymer concentration is 1 mg mL1. The curve displays two singular points: 1, intersection point of the binodal (Tt,1); 2, intersection point of line of the coexistence of three phases; Dtcp < 0, total heat capacity increment of the phase transitions 1 and 2. The temperature Tt,1 coincides with the cloud point temperature of the system. The dash line is a linear approximation of the pre-transition part of the curve.
at the given system composition, respectively. In addition, an important feature of the temperature dependence of partial heat capacity of PVME is the fact that the partial heat capacity after completion of the phase separation is clearly lower than that in the initial homogeneous state of the system. In other words, the total heat capacity increment of the transitions 1 and 2 is negative, Dtcp < 0. This effect is typical of amphiphilic polymers and gels. For example, it has been observed for cross-linked and linear PNIPAM [8,10], poly(N-vinylcaprolactam) [9], and NIPAM-styrene sulfonate copolymers of various composition and structure [11]. A negative value of the heat capacity increment is an evident indication for the
Fig. 3. Thermodynamic parameters of the phase separation of aqueous solutions of PVME under normal pressure: (a) 1, binodal temperature (Tt,1); 2, temperature of the coexistence of three phases (Tt,2 ¼ 36.8 ± 0.1 C); (b) total enthalpy of the phase separation (88.0 ± 1.2 J g1); (c) total heat capacity increment of the phase separation (1.0 ± 0.1 J g1 K1).
286
V.Y. Grinberg et al. / Polymer 87 (2016) 283e289
weak tendency to increase when the polymer concentration decreases in the studied range. On the other hand, the temperature Tt,2 remains unchanged (36.8 ± 0.1 С). The transition enthalpy and heat capacity increment do not depend on the polymer concentration (Dth ¼ 88.0 ± 1.2 J g1; Dtcp¼1.0 ± 0.1 J g1 K1). Note that in respect of the transition parameters PVME far exceeds other thermoresponsive polymers [8e11]. It is well-known that there is a fundamental relation between enthalpies and heat capacity increments of many transitions including protein denaturation, which are associated with transfer of apolar molecules or groups from a parent environment to water [20e22]:
Dt h ¼ Dt cp T TH* þ Dh0
(1)
where T is an arbitrary reference temperature; TH* is the so-called convergence temperature, at which the contribution of hydrophobic hydration to the transition enthalpy vanishes; and term Dth0 takes into account the contribution of van der Waals interactions or hydrogen bonds to the transition enthalpy. There are different estimates of the convergence temperature that are rather close to each other. Nevertheless, a value of this temperature, TH* ¼ 110 C, determined from calorimetric data for small globular proteins by Privalov and Khechinashvili [20] seems to be preferable. We used Eq (1) for correlation of the data for PVME and other thermoresponsive polymers previously studied [8e11] at a temperature T¼ 34.7 C, which is an averaging of the transition temperatures of the polymers under consideration. As shown in Fig. 4 there is a linear correlation between the transition enthalpy and heat capacity increment for thermoresponsive polymers of different composition and structure. From the slope of the correlation line it is followed that the convergence temperature TH* is 111 C. Our estimate of TH* coincides perfectly with the convergence temperature determined by Privalov and Khechinashvili for a number of globular proteins [20]. This fact seems to be of general significance for understanding origin and main driving forces of the thermoresponsive polymer self-organization. It suggests a deep
Fig. 4. Correlation between the LCST transition parameters of some thermoresponsive polymers according to Eq. (1): PVME (1), PNIPAM (2) [11], PNIPAM (3) [10], NIPAM gel (4) [8], poly(N-vinylcaprolactam) (5) [9], NIPAM-styrene sulfonate (2%) copolymer (6) [11], NIPAM-styrene sulfonate (20%) copolymer (7) [11], N-vinyicaprolactam-MAAc (12%) copolymer (8) [9], N-vinyicaprolactam-MAAc (18%) copolymer (9) [9]. The slope of the correlation line indicates that the convergence temperature TH* is 111 C. Correlation coefficient is 0.945.
similarity of hydrophobic hydration of polymer chains composed of different hydrophobic groups. Contribution of hydrophobic hydration into the transition energetics is apparently not influenced by hydrophilic part of a thermoresponsive macromolecule. 3.2. Phase separation of aqueous solutions of PVME at high pressures This research was carried out in a pressure range up to 170 MPa at different concentrations of the polymer from 1 to 11 mg mL1 (0.1e1.1%). Typical excess heat capacity functions of phase separation at various pressures are compared in Fig. 5. The singular points (crossing points with the binodal and the line of coexistence of three phases) mentioned above are clearly seen on all curves. When pressure increases, the resolution of these points becomes more and more descriptive while a heat response from the change in phase state of the system decreases rapidly. Fig. 6 illustrates the pressure effects on the calorimetric parameters of phase separation of aqueous PVME solutions. The binodal temperature Tt,1 decreases by 10 С, the three-phases coexistence temperature Tt,2 increases by 15 C and the total transition enthalpy is reduced 1.5 fold upon increase in pressure. Significantly, the pressure dependences of the calorimetric parameters obtained at different polymer concentrations coincide within the experimental errors. A strict interpretation of dependences of the phase separation
Fig. 5. Excess heat capacity functions of phase separation of aqueous solutions of PVME under different pressures, MPa: 0.0981 (a), 24.2 (b), 47.0 (c), 69.7 (d). The curves are arbitrarily shifted along the ordinate axis to avoid overlap. The singular points of curves: 1, intersection point of the binodal; 2, intersection point of the line of coexistence of three phases. Polymer concentration is of 4.26 mg mL1.
V.Y. Grinberg et al. / Polymer 87 (2016) 283e289
vln Tt Dt v y Dt h vp
287
(2)
where Tt is the characteristic transition temperature; Dtv is the transition change in the partial volume of polymer; Dth is the transition enthalpy. In our case there are two consequent phase transitions with the characteristic temperatures Tt,1 and Tt,2. For convenience of consideration, their pressure dependences are given in the semilog form: ln Tt,1 ¼ f(p) and ln Tt,2 ¼ f(p), in Fig. 7. We can write the corresponding ClausiuseClayperon equation for each of them:
vln Tt;1 Dt v1 y vp Dt h1
(3)
vln Tt;2 Dt v2 y vp Dt h2
(4)
where Dtv1 and Dtv2 are the changes in the partial volume of polymer as result of the crossing of the binodal and the line of coexistence of three phases (the phase transitions 1 and 2, respectively); Dth1 andDth2 are the enthalpies of these transitions. The obtained calorimetric data do not allow one to estimate the
Fig. 6. Calorimetric parameters of phase separation of aqueous solutions of PVME vs. pressure: (a) the temperature of the binodal; (b) the temperature of coexistence of three phases; (c) total transition enthalpy. Polymer concentration, mg mL1: 1.0 (1), 2.0 (2), 4.3 (3) and 10.6 (4).
temperature of solutions (in particular, of aqueous solutions of polymers) on pressure is a specific theoretical problem. However we believe that for a qualitative consideration of the phenomenon it is possible to accept this dependence in the form of the ClausiuseClayperon equation [23]:
Fig. 7. Semi-log plots of the characteristic temperatures of the phase diagram of aqueous solutions of PVME on pressure: (a) the binodal temperature; (b) the temperature of coexistence of three phases. Polymer concentration, mg mL1: 1.0 (1), 2.0 (2), 4.3 (3), 10.6 (4).
288
V.Y. Grinberg et al. / Polymer 87 (2016) 283e289
enthalpies Dth1 and Dth2 because of strong overlapping the transitions 1 and 2. Nevertheless, it is quite evident that both enthalpies are positive, that is, Dth1 > 0 и Dth2 > 0. It follows that a slope of the pressure dependence of logarithm of the characteristic temperature will be determined by a sign of the transition increment of partial volume of polymer. The slope of the dependence ln Tt,1 ¼ f(p) is negative. Consequently, Dtv1 < 0. In contrast, the slope of the dependence ln Tt,2 ¼ f(p) is positive and correspondingly Dtv2 > 0. Thus the increments of partial volume of polymer associated with the consequent phase transitions, which the diluted aqueous solutions of PVME undergo upon heating, have opposite signs. This difference seems to be of a principal importance. It suggests that these phase transitions are of different nature. It is still difficult to say about a nature of the first transition. In contrast, the nature of the second transition is in general clear, since the positive partial volume increment of polymer is typical of the transitions accompanied by a change in accessibility of apolar residues of the polymer to water molecules, e.g. for denaturation of globular proteins [24]. It should be noted that the theoretical models elaborated for description of the phase behaviour of aqueous solutions of PVME [18,19] consider the consequent transitions in this system in framework of a single equation of state. So they do not distinguish these transitions by their nature. Our data emphasizing the differences in the nature of the transitions indicate a need of elaboration of new theoretical approaches for description of very unusual properties of PVME. The transition heat capacity increment is one of the key thermodynamic parameters helping to understand a nature of the transition [25]. Therefore it was of importance to determine the heat capacity increment of the phase separation of aqueous solutions of PVME under different pressures. We could performed such measurements only at a relatively high polymer concentration of 10.6 mg mL1 (~1.1%) because of some technical problems. Such a concentration allowed determination of the transition heat capacity increment with a good precision but without simultaneous determination of the transition enthalpy because of cutting the top of the heat capacity peak due to the saturation of the thermal sensor of the calorimeter at excessively high heat absorption of the sample. The temperature dependence of the apparent partial heat capacity of PVME at pressure 23.5 MPa is presented in Fig. 8a. This figure underlines a complex calorimetric profile of the phase separation: the presence of the first singular point associated with the transition of the system through the binodal and a clear decrease in the partial heat capacity of the polymer as a result of phase separation. Fig. 8b shows that the transition heat capacity increment remains unchanged in the studied pressure interval, Dtcp ¼ 1.2 ± 0.1 J g1 K1. This value agrees well with the result of determination of the heat capacity increment at normal pressure and low polymer concentrations.
Fig. 8. (a) Apparent partial heat capacity of PVME in an aqueous solution under pressure 23.5 MPa. Polymer concentration is 10.6 mg mL1. The binodal point is shown by an empty point. A top of the curve is cut off as a result of saturation of the thermal sensor of the calorimeter. (b) Total LCST transition heat capacity increment of PVME vs. pressure. Its average value is 1.2 ± 0.1 J g1 K1.
depend on the polymer concentration and pressure. A linear correlation between the enthalpies and heat capacity increments of the LCST transitions of a number of thermoresponsive polymers including poly(vinyl methyl ether) is found. It shows that the convergence temperature TH* , at which the contribution of hydrophobic hydration to energetics of the LCST transitions vanishes, is close to the convergence temperature of globular proteins (TH* ¼ 110 С).
4. Conclusion The diluted aqueous solutions of poly(vinyl methyl ether) undergo the consequent phase transitions upon heating. The first transition temperature decreases with increasing the polymer concentration and pressure. The second transition temperature does not depend on the polymer concentration but increases with increasing the pressure. The first transition is accompanied by the decrease and the second one - by the increase in the partial specific volume of the polymer. This principal difference seems to reveal that natures of these transitions differ drastically. The total enthalpy of both transitions does not depend on the polymer concentration and decreases with increasing pressure. The total heat capacity increment of the transitions is negative. It does not
Acknowledgement The financial support from the Russian Foundation for Basic Research (project 13-03-00574) is greatly appreciated. References [1] [2] [3] [4] [5] [6]
H.G. Schild, Prog. Polym. Sci. 17 (2) (1992) 163e249. P. Alexandridis, T.A. Hatton, Colloids Surfaces A 96 (1e2) (1995) 1e46. V.O. Aseyev, H. Tenhu, F.M. Winnik, Adv. Polym. Sci. 196 (2006) 1e85. V. Aseyev, H. Tenhu, F.M. Winnik, Adv. Polym. Sci. 242 (2011) 29e89. E.S. Gil, S.M. Hudson, Prog. Polym. Sci. 29 (12) (2004) 1173e1222. C.D.H. Alarcon, S. Pennadam, C. Alexander, Chem. Soc. Rev. 34 (3) (2005) 276e285.
V.Y. Grinberg et al. / Polymer 87 (2016) 283e289 [7] N.V. Grinberg, A.S. Dubovik, V.Y. Grinberg, D.V. Kuznetsov, E.E. Makhaeva, A.Y. Grosberg, T. Tanaka, Macromolecules 32 (5) (1999) 1471e1475. [8] V.Y. Grinberg, A.S. Dubovik, D.V. Kuznetsov, N.V. Grinberg, A.Y. Grosberg, T. Tanaka, Macromolecules 33 (23) (2000) 8685e8692. [9] A.S. Dubovik, E.E. Makhaeva, V.Y. Grinberg, A.R. Khokhlov, Macromol. Chem. Phys. 206 (9) (2005) 915e928. [10] A.S. Dubovik, N.V. Grinberg, V.Y. Grinberg, Polym. Sci. Ser. A 52 (6) (2010) 565e573. [11] V.Y. Grinberg, T.V. Burova, N.V. Grinberg, A.S. Dubovik, I.G. Plaschina, T.V. Laptinskaya, Y. Xiong, P. Yao, A.R. Khokhlov, Macromol. Chem. Phys. 216 (24) (2015) 2344e2355. [12] V.Y. Grinberg, A.A. Senin, N.V. Grinberg, T.V. Burova, A.S. Dubovik, S.A. Potekhin, I.Y. Erukhimovich, Polymer 64 (2015) 14e18. [13] S.A. Potekhin, Polym. Sci. Ser. C 54 (1) (2012) 108e115. [14] E. Loozen, E. Nies, K. Heremans, H. Berghmans, J. Phys. Chem. B 110 (15) (2006) 7793e7802.
289
[15] C. Querner, T. Schmidt, K.F. Arndt, Langmuir 20 (7) (2004) 2883e2889. [16] A.A. Senin, S.A. Potekhin, E.I. Tiktopulo, V.V. Filomonov, J. Therm, Anal. Calorim. 62 (1) (2000) 153e160. [17] P.L. Privalov, S.A. Potekhin, Methods Enzymol. 131 (1986) 4e51. €fer-Soenen, R. Moerkerke, H. Berghmans, R. Koningsveld, K. Dusek, [18] H. Scha K. Solc, Macromolecules 30 (3) (1997) 410e416. [19] K. Van Durme, G. Van Assche, E. Nies, B. Van Mele, J. Phys, Chem. B 111 (6) (2007) 1288e1295. [20] P.L. Privalov, N.N. Khechinashvili, J. Mol. Biol. 86 (3) (1974) 665e684. [21] R.L. Baldwin, N. Muller, P. Natl, Acad. Sci. U. S. A. 89 (15) (1992) 7110e7113. [22] K.P. Murphy, E. Freire, Adv. Protein Chem. 43 (1992) 313e361. [23] I. Prigogine, R. Defay, Chemical Thermodynamics, Longmans Green Co., London-N.Y.-Toronto, 1954. [24] M. Gross, R. Jaenicke, Eur. J. Biochem. 221 (2) (1994) 617e630. [25] G.I. Makhatadze, P.L. Privalov, Adv. Protein Chem. 47 (1995) 307e425.