Quasichemical Approach to pH Shifts in Frozen Phosphate

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Thermodynamics, Transport, and Fluid Mechanics

Quasichemical Approach to pH Shifts in Frozen Phosphate Buffers Yusuke Okada, Makoto Uyama, Makoto Harada, and Tetsuo Okada Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.9b03755 • Publication Date (Web): 07 Sep 2019 Downloaded from pubs.acs.org on September 7, 2019

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Industrial & Engineering Chemistry Research

Quasichemical Approach to pH Shifts in Frozen Phosphate Buffers

Yusuke Okada,1 Makoto Uyama,2 Makoto Harada,1 and Tetsuo Okada1*

1 Department

of Chemistry, Tokyo Institute of Technology, Meguro-ku, Tokyo 152-8551,

Japan. 2

Shiseido Global Innovation Center, 1-2-11, Takashima, Nishi-ku, Yokohama 220-0011,

Japan.

*[email protected] Phone and Fax: +81-3-5734-2612

1 ACS Paragon Plus Environment

Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract The shifts in the pH of buffer solutions upon freezing have received much attention particularly in the life sciences, as such pH variation during freezing may damage biological samples, biomolecules, and pharmaceuticals. The understanding and prediction of said pH changes upon freezing are essential to utilize buffer solutions in a wide temperature range, including subzero temperatures. Phosphate is of particular importance for aqueous buffer preparation as it covers a wide pH range and displays high biocompatibility. However, the phase behavior and pH changes in phosphate buffers at subzero temperatures are very complex due to the variety of species involved in the phase and acid–base equilibria. This paper focuses on the interpretation of the pH changes in phosphate buffers under freezing conditions using an extended universal quasichemical (EUQ) model. This model has been previously applied to understand the phase behavior (solid precipitation) in phosphate buffers at subzero temperatures, but not to the calculation of the pH of the liquid phase (freeze-concentrated solution, FCS) that coexists with ice and salt precipitate. Since the EUQ model provides activity coefficients for all of the components in the system, not only the phase behavior but also the pH value can be estimated. The calculated pH values have been compared to experimental values and are interpreted from the viewpoints of salt deposition, salt enrichment in the FCS, and supercooling effects.


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Introduction Freezing is an important process in the natural environment,1-3 life sciences,4 pharmaceutics,5-6 engineering,7-9 industry, and laboratory experiments. The solutes contained in aqueous solutions are mostly expelled from the ice crystals upon freezing. Water-soluble solutes remain thus concentrated in the liquid phase (freeze-concentrated solution, FCS) present at the ice grain boundaries. The FCS has been employed for separation,10-12 detection,13 enrichment,14-15 and reactions;16 in addition, its unique physicochemical properties have been reported in various instances.17-18 Some reactions are, for example, accelerated in the FCS compared to typical bulk solutions.16, 19-20 The FCS acts as a reactor in the natural environment and is involved in the global circulation of, e.g., nitrogen oxides and related compounds.20-21 The freezing behavior of a simple binary system such as water/NaCl is well characterized by a phase diagram. The FCS in this system is a concentrated NaCl solution. The freezing point depression curve is expressed in this case by the activities of water and the constituent ions, i.e., Na+ and Cl–. Thermodynamics predicts that the components form a solid phase (i.e., ice and NaCl·2H2O) and that an FCS does no longer exist below the eutectic temperature of the system (251.8 K).22 However, some studies have indicated that the FCS may remain even below the eutectic point, particularly in the case of diluted solutions.11,

23-24

Studies from various perspectives are thus still required for full

understanding of such complex systems. Phosphate buffers are often used in life sciences to maintain the physiological pH at 3 ACS Paragon Plus Environment


typically 7.4.25 Although the samples and compounds used in such studies are stored at subzero temperatures, freezing may damage the biological samples via degradation or denaturation of biomolecules as a result of ice crystallization and pH changes in the FCS.26

Since phosphate buffers are not necessarily good media for freeze preservation

of biomaterials considering the observed changes in their pH, the incorporation of appropriate additives has been extensively investigated. Bovine serum albumin, dimethyl sulfoxide, sugars, and glycerol are often added as cryoprotectants to prevent damage of biological samples.26-27 The pH changes induced by freezing of phosphate buffers cause indeed damage to biomaterials present in the system.28 For example, Gomez et al. measured the pH of phosphate buffers under frozen conditions and found a pH drop of ~3.29 The mechanism of the pH shift in phosphate buffers by freezing has been discussed from the viewpoint of solid phase deposition, rather than a change in the FCS composition.29-32 The activity of all the components should be appropriately determined to explain the phase diagrams, which involve solid–liquid equilibria, and also to understand the observed pH shifts at subzero temperatures. A combinatorial approach of theoretical and experimental methods is necessary to interpret such complex systems. Lin et al.33 compared several models: the electrolyte non-random two-liquid model, mixed solvent


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electrolyte model, and extended universal quasichemical (EUQ) model, in terms of the reproduction of experimentally known solid–liquid equilibria. No model could reproduce the experimental data in terms of the solid phase composition and solubility curves with precision. However, the EUQ model has been applied to the explanation of the freezing behavior of aqueous electrolytes and has provided relatively good predictions. An advantage of this approach is that it requires fewer parameters than other equivalent models.33-45 In this method, the original universal quasichemical model is combined with long-range interactions of ions to reasonably represent aqueous electrolyte solutions. Christensen and Thomsen45 have interpreted the solid–liquid equilibria of phosphate buffers using this model. However, to the best of our knowledge, no reports exist on the study of the variation of the FCS pH during solid phase deposition using this model. Recent developments in pH measurement techniques have allowed the determination of pH under severe conditions including subzero temperatures.29,

46-47

Interesting

phenomena, e.g., pH oscillation in frozen buffers,46-47 were identified during pH measurements in frozen solutions using such a technique. Phosphate buffers cover a wide pH range and display rather high biocompatibility. However, as noted above, freezing causes precipitation of the salt, as well as dramatic changes in the pH of phosphate buffers. Understanding the mechanism will allow us to predict freeze-induced pH changes and to



prevent them by modifying the solution composition. Both acid–base and phase equilibria should be simultaneously evaluated to interpret all the phenomena occurring in the solution during freezing. The description of the entire system is very complex as many species, i.e., H2O, H+, OH−, Na+ (K+), H3PO4, H2PO4−, and HPO42−, need to be considered.48-49 In this work, we have measured the pH of typical phosphate buffers in the temperature range of 258.15–298.15 K and interpreted the pH changes in the FCS induced by freezing using the EUQ model.

Methods Phthalate, phosphate, and tetraborate pH standard solutions were purchased from Wako Pure Chemical Industries Ltd. (Osaka, Japan). Water was purified by a Milli-Q Reagent Water System, (Millipore Co., Bedford, MA). Sample solutions prepared in MilliQ water were sonicated for at least 10 min to remove any dissolved gases before pH measurement. The solution (15 mL) was put in a glass vessel fitted in a copper tube. The gap between the glass vessel and copper tube was filled with ethylene glycol. So as to maintain a constant temperature of the sample, the copper tube was placed on a Peltier array driven by a Cell System Peltier controller model TDC-2030R. The sample temperature was monitored with a platinum resistance thermometer immersed in the


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solution. The temperature fluctuation was smaller than ±0.05 °C. The reverse side of the Peltier array was cooled by a chiller. A low-temperature pH electrode (InLab® Cool, Mettler Toledo, Switzerland) was placed in the center of the sample glass vessel and connected to a pH meter (S40 SevenMultiTM pH meter, Mettler Toledo) to monitor the electric potential difference. A Friscolyte-B® (Mettler Toledo) was used as the reference electrode. These electrodes were immersed in a solution, and then the entire system was frozen when pH of a frozen solution was monitored. The Peltier controller and pH meter were connected to a computer to allow simultaneous monitoring of the time-changes in the temperature and electrode potential difference (ΔETC). After equilibration at 293 K, the sample solution was cooled to 253 K and then warmed to 293 K at a rate of 0.03 K s–1. As shown below, this rate was often affected by the latent heat from the phase transition of water. In addition to the time evolution measurements of ΔETC, ΔETE was measured at constant temperature. After complete freezing at 253 K, the sample temperature was increased to the desired value and ΔETE was measured after reaching thermal equilibrium, i.e., the Peltier temperature agreed with that of the sample. After the thermal equilibrium was reached, ΔE became constant. The pH was calculated from the ΔE value using the calibration curves constructed using standard solutions at pH 4, 7, and 9 and 273 and 298 K. The slope was proportional to the temperature; the Nernstian



response was confirmed. In both cases, ΔE = 0 occurred at pH 7.0. The calibration graphs obtained for unfrozen solutions were extended to measurements at subzero temperatures by assuming ΔE = 0 at pH 7.0 and a Nernstian slope. ΔETC and ΔETE values were converted into pHTC and pHTE, respectively. An Olympus microscope Model DSU-BX61WI was used to obtain fluorescence images of the FCS developed in frozen samples. The microscope was equipped with a spinning disk confocal system, which provided three-dimensional confocal images with a Hg-lamp as the light source.

The fluorescence was monitored with a CCD camera

Model C9100-13 (Hamamatsu Photonics). objective was used for all images.

A water-immersion ×20 (N/A = 0.5)

For fluorescence observation with FL, an optical U-

MWIB3 filter (Olympus) was used with excitation (λex) and emission (λem) wavelengths of 460495 and 510 nm, respectively.

For fluorescence observation with RH, a U-

MWIG3 filter (Olympus) was used with λex = 530550 nm and λem = 575 nm. The concentration of FL or RH in the original solutions before freezing was 100 nM.

Results and Discussion EUQ model including acid–base equilibria In the EUQ model, the activity coefficients (γ) are given by the sum of three terms: combinatorial, residual, and Debye−Hückel terms.35-39, 43, 45 The combinatorial term (𝛾𝐶𝑖), 8 ACS Paragon Plus Environment

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which corrects the departure from the ideal solution taking into account the shape and size of an ion, is a function of the mole fractions (x), as expressed by: 𝜙𝑖

𝜙𝑖

𝑟𝑖

𝑟𝑖

[

z

𝜙𝑖

𝜙𝑖

𝑟𝑖𝑞𝑤

]

𝑟𝑖𝑞𝑤

ln 𝛾𝐶𝑖 = ln 𝑥𝑖 ― 𝑥𝑖 ― ln 𝑟𝑤 + 𝑟𝑤 ― 2𝑞𝑖 ln 𝜃𝑖 ― 𝜃𝑖 ― ln 𝑟𝑤𝑞𝑖 + 𝑟𝑤𝑞𝑖 𝜙𝑖 =

𝑥𝑖𝑟𝑖

, 𝜃𝑖 =

∑𝑘𝑥𝑘𝑟𝑘

(1)

𝑥𝑖𝑞𝑖 ∑𝑘𝑥𝑘𝑞𝑘

where r and q are the volume and surface area parameters in the system, and z is the coordination number, which is normally set to 10. The residual term (𝛾𝑅𝑖) is the enthalpic term that describes short-range molecular interactions. This term involves a binary interaction parameter, u , which depends on the temperature and concentration. This value is obtained from the phase diagram or other experimental data. In this work, its concentration dependence was ignored to reduce the number of parameters.

[

]

𝜃𝑘𝜓𝑖𝑘

ln 𝛾𝑅𝑖 = 𝑞𝑖 ― ln (∑𝑘𝜃𝑘𝜓𝑘𝑖) ― ∑𝑘∑ 𝜃 𝜓 + ln 𝜓𝑤𝑖 + 𝜓𝑖𝑤

(

𝜓𝑖𝑗 = exp ―

𝑙 𝑖 𝑙𝑘

(𝑢𝑗𝑖∘ ― 𝑢𝑖𝑖∘ ) + (𝑢𝑡𝑗𝑖 ― 𝑢𝑡𝑖𝑖)(𝑇 ― 298.15)

(2)

)

𝑇

, 𝑢𝑖𝑗∘ ,𝑡 = 𝑢𝑗𝑖∘ ,𝑡

The parameters used in this work are listed in Tables S1 and S2. Finally, the Debye−Hückel term (𝛾𝐷𝑤 ― 𝐻) describes long-range molecular (water−water, water−ion, and ion−ion) interactions. The Debye−Hückel parameter, A, includes the relative permittivity and density, which depend on the temperature and concentration. In particular, since the relative permittivity largely depends on the temperature, the dependence on the ion concentration was here ignored. It was in turn represented by a cubic polynomial with respect to the temperature. On the other hand, the 9 ACS Paragon Plus Environment


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density largely depends on the ion concentration and, therefore, has been expressed by a fourth-order polynomial with respect to the concentration. The temperature dependence of the density and permittivity of water is shown by the fitted curves in Figure S1.50 For an ion

i, 𝑧2𝑖 𝐴 𝐼

𝐹3

𝜌

ln 𝛾𝐷𝑖 ― 𝐻 = ― 1 + 𝑏 𝐼, 𝐴 = 4𝜋𝑁𝐴

(3)

2(𝑅𝜖0𝜖𝑟𝑇)3

For water, ln 𝛾𝐷𝑤 ― 𝐻 =

𝑀𝑤2𝐴 𝑏3

[1 + 𝑏

𝐼―

1 1+𝑏 𝐼

]

― 2log (1 + 𝑏 𝐼)

(4)

where F, NA, R, and T are Faraday constant, Avogadro’s number, gas constant, and temperature, respectively, ε0 and εr are the permittivity of vacuum and relative permittivity of the medium, ρ is the density of solution, M w is molar mass of water, b is equal to 1.5, I is the ionic strength based on molality, and z is the charge of the ion. Based on the activity of each species present in the system, the phase behavior was evaluated. The formation of a solid was evaluated by comparing the chemical potential of the solid phase with the sum of the chemical potentials of the related species in solution, e.g., a solution is frozen when μice < μwater, whereas freezing does not occur when μice > μwater. This approach was applied to the formation of other solids. In this work, we have assumed that trivalent phosphate ion is not present in the system because the related parameters are rather ambiguous because of lack of relevant experimental data. In addition, it is thus difficult to calculate precisely the very low concentrations of H+ in basic solutions. Therefore, the discussion is confined to neutral


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or acidic solutions. The concentration units (molar, molal, wt%, and under ratio) were mutually converted using the solution density and molecular mass of the solutes. In this paper, wt% or molar (M) is used as most of the literature values are reported in those units. Since the activity coefficients were calculated from the above procedure, acid–base calculations eventually gave the activity of hydrogen ions. The activity-based dissociation constants of phosphoric acid at subzero temperatures were derived from the standard chemical potential of each species: 𝜇° = Δf𝐻 ∘ + 𝐶p∘ (𝑇 ― 298.15) ―𝑇

(

( Δ f𝐻 ∘ ― Δ f𝐺 ∘ ) 298.15

+ 𝐶p∘ ln

(

𝑇

))

298.15

(5)

where Δf𝐻 ∘ , Δf𝐺 ∘ , and 𝐶p∘ are the standard enthalpy of formation, the standard Gibbs energy of formation, and the standard heat capacity, respectively. The temperature dependence of the equilibrium constants was calculated using the values listed in Table S1,51-53 and the results are shown in Figure S2.

Phase diagrams of phosphate solutions and buffers The EUQ model has been extensively employed to reproduce the phase diagrams of various systems including liquid–gas,35, 38-39 liquid–solid,33, 43-45, 54 and liquid–liquid systems.40-42 A number of combinations of parameters have been evaluated in terms of the agreements of experimental data with calculated phase behaviors.33, 43, 45 In this study, the parameters listed in Tables S1 and S2 were used to predict the behavior of the components of phosphate buffers using the EUQ model. The binary phase diagrams of water and one of the phosphate salts were first studied to validate the present calculations. 11 ACS Paragon Plus Environment


The FCS composition was assumed to be uniform for all of the following calculations. This assumption is basically applicable to usual cases but may be inapplicable to large systems. Figure 1 compares the results of the calculations with experimental values taken from the literature.55 The calculations reproduce rather well the phase diagrams, albeit with some differences in the solubility curves, e.g., in the water/K2HPO4 system. Since the present study focuses on the solution composition at subzero temperatures around the eutectic point (Teu), the initial concentration was assumed to be lower than the eutectic concentration (ceu). Therefore, small disagreements in the solubility curves are not significant for the corresponding discussions. The literature Teu and ceu values are compared to the corresponding values obtained from the present calculations in Table 1.31 For aqueous NaH2PO4, KH2PO4, Na2HPO4, and K2HPO4 solutions, the eutectic temperatures have been reported as 263.5, 270.5, 272.7, and 259.5 K, respectively, while the calculated values are 262.7, 270.5, 272.7, and 259.6 K, respectively. The calculations thus reproduce satisfactorily the experimental Teu. Similarly, the experimental ceu values are also well predicted by the present calculations. Thus, the phase equilibria for binary mixtures of water and a single phosphate salt are satisfactorily described by the present model, supporting its reasonable application to the solid–liquid equilibria of these systems. The phase diagrams of AH2PO4/B2HPO4 (A, B = Na+ or K+) systems were also examined. Figure 2 shows the phase diagrams of ternary water/AH2PO4/B2HPO4 systems, in which the temperature is given by contours. The solid–liquid boundaries are shown as valleys in these three-dimensional representations, which are expressed by red curves in 12 ACS Paragon Plus Environment

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the figures. The eutectic points are shown as the intersections of the red curves on the simulated phase diagrams. For example, the eutectic point for water/NaH2PO4/Na2HPO4 is found at cNaH2PO4 = 32 wt% and cNa2HPO4 = 1.8 wt% at 262 K. A complex phase diagram was obtained for water/NaH2PO4/K2HPO4, as shown in Figure 2D. In this system, Na2HPO4, which was not added to the original solution, is deposited immediately after freezing. As a result, two eutectic points are predicted depending on the initial solution composition. The eutectic points estimated from the calculations are listed in Table 2 together with the literature values.56 The present calculations reproduce well the experimental values, though some differences exist, particularly in the ceu values. Thus, although small disagreements between the calculated and experimental values are seen in some cases, we conclude that the present calculations are suitable for further discussion of the pH of FCSs.

pH changes of phosphate solutions and buffers upon freezing Since it is well known that Na2HPO4·12H2O is first deposited from Na+ phosphate buffers when the temperature decreases, the pH change caused by this event has been often discussed in the literature.29 Gomez et al. reported that the pH value of a 100 mM NaH2PO4/Na2HPO4 buffer decreased from 7.4 to 4 upon freezing at 263 K and concluded that this change was induced by the precipitation of Na2HPO4·12H2O.29 Murase and Franks31, 57 studied phosphate solutions by differential scanning calorimetry (DSC) and confirmed the precipitation of some phosphate salts upon freezing. These studies 13 ACS Paragon Plus Environment


obviously suggest that the pH changes in frozen aqueous phosphate buffers are mainly caused by the deposition of salts. Nevertheless, the phenomena occurring in the system at subzero temperatures are more complex than intuitively expected. The pH changes of phosphate solutions and buffers at subzero temperatures were measured to evaluate the applicability of the present model. Figures S3 and S4 show the relationships between ETC and temperature for binary (50 mM phosphate salt) and ternary (1:1 AH2PO4/B2HPO4, 25 mM each) systems (see Methods for details of measurements). The lowest temperature was set to 253 K. The measured ETC values were converted into pH (pHTC), as shown in Figures 3 (binary) and 4 (ternary). The pH values measured at thermal equilibrium (pHTE) are also plotted in these figures. The pHTE values basically fall on the pHTC curves, although small differences exist in some cases. For example, the pHTE is lower than the corresponding pHTC value in the water/AH2PO4 systems. This suggests that the equilibrium was not reached during pH measurement at variable temperatures. Only a slight increase in the pH (

Quasichemical Approach to pH Shifts in Frozen Phosphate

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