Article pubs.acs.org/JPCB
Thermodynamic Profiles of Salt Effects on a Host−Guest System: New Insight into the Hofmeister Effect Corinne L. D. Gibb, Estelle E. Oertling, Santhosh Velaga, and Bruce C. Gibb* Department of Chemistry, Tulane University, New Orleans, Louisiana 70118, United States S Supporting Information *
ABSTRACT: Isothermal titration calorimetry was used to probe how salts influence the thermodynamics of binding of guests to cavitand 1. Studies involved six Hofmeister salts covering the range of salting-in to strongly salting-out. The latter were found to reduce affinity. The cause of this was competitive binding of the weakly solvated anion to the hydrophobic pocket of the host. At the other extreme of the Hofmeister series, salts increased guest affinity. Two factors for this were evident. At low concentrations the data fitted a previously reported model that accounts for cation condensation to the outer carboxylates of the host (Carnagie, R.; Gibb, C. L. D.; Gibb, B. C., Angew. Chem., Int. Ed. 2014, 53 (43), 11498−11500). At higher concentrations, an as of yet unidentified contribution was observed that was noted to be guest dependent. Midcontinuum salts such as NaClO3 were found to enhance affinity at low concentrations, but weaken it at high concentrations; a nonmonotonic trend attributed to the aforementioned competing phenomena. In combination with previous work, the data presented here reveal that the Hofmeister effect evident in this system can be mostly attributed to solute−salt interactions.
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INTRODUCTION Aqueous solutions are ubiquitous in the biosphere, atmosphere, hydrosphere, and (at least)1 the palpable lithosphere, and consequently a thorough understanding of their properties is of importance to all sciences. A frequent observation in studies of the chemistry of aqueous solutions is the Hofmeister effect. Franz Hofmeister, in his landmark 1888 paper on the solubility of eggwhite proteins,2,3 noted that some salts decreased the solubility of proteins, whilst others did the opposite. In ordering the salts in terms of their precipitation power he formulated the first examples of what are now known as the Hofmeister series: one for cations and one for anions (Figure 1a).4 Subsequent to these initial studies, the Hofmeister series has been observed in at least 38 macroscopic phenomena pertaining to aqueous solutions.5−8 For example, if salts are ordered according to their ability to increase surface tension or increase (or decrease) surface potential very similar sequences are observed. However, despite being documented for over 125 years, there is as of yet no thorough explanation of the Hofmeister effect. At a most general level, for a three-component mixture of water, salt, and an organic co-solute there are six types of noncovalent interactions present in solution (Figure 1b), and it is the overall balance between these that controls the behavior and properties of the solution. Which noncovalent interactions dominate to engender the Hofmeister effect? The answer is likely system specific, depending on the nature of the salt and the structural features of the solute. However, even if this is the case there are likely yet to be determined semiquantitative guidelines © 2015 American Chemical Society
or quantitative models that will prove of utility in predicting or explaining properties of aqueous solutions. Historically, probing the Hofmeister effect has relied primarily on bulk-scale measurements. For example, at one of the simplest water interfaces, the air−water interface, early studies focused on surface tension and surface potential measurements for different concentrations of a range of salts.9,10 However, the lack of resolution of such studies, i.e., their inability to reveal what occurs at the molecular- or nanoscale, has led to controversy. For example, whereas the reactivity of aerosols dictates that certain anions must accumulate at the air−water interface,11−13 the measured increase in surface tension as a function of increasing salt concentration can only be accounted for by the Gibbs isotherm if there is a net depletion of ions from the interface.14 The actuality that dispelled this apparent contradiction was only relatively recently identified with a variety of empirical15−18 and computational studies6,19,20 identifying nonmonotonic concentration-profiles of ions at the air−water interface. For example, with sodium iodide it has been determined that iodide concentrations at the air−water interface are higher than the bulk but that there is a depletion layer underneath the immediate surface. In combination with a depletion layer of sodium ions at the air−water interface, but a higher than bulk concentration some 0.5 nm away from the interface, the net concentration of Received: February 19, 2015 Revised: April 2, 2015 Published: April 16, 2015 5624
DOI: 10.1021/acs.jpcb.5b01708 J. Phys. Chem. B 2015, 119, 5624−5638
Article
The Journal of Physical Chemistry B
Figure 1. (a) Typical Hofmeister series for anions and how they affect three representative physical properties. Length and direction of arrow correspond to the magnitude and direction of change, respectively. (b) Possible noncovalent interactions (blue lines) between components of an aqueous solution of a salt and a solute.
Figure 2. (a) Three representations of octa-acid host 1: chemical structure (left), space-filling model from the same perspective (center), and “plan” view looking down into the hydrophobic pocket (right). (b) To approximately the same scale, space-filling models of conjugate acids of, respectively, guests 2, 3, 4, and 5 (see main text).
Thus, while still undoubtedly playing a role in the Hofmeister effect, ion−water and ion−ion interactions apparently do not dominate. The possibility that other noncovalent interactions (Figure 1b) may be significant in the Hofmeister effect was explored in the 1960s and 1970, with, for example, the study of the interaction of lithium ions with amides groups,35,36 and the measurement of the thermodynamics of salt binding to polyacrylamide and polystyrene solid supports.37 Further studies on this topic were relatively infrequent, until around the turn of the millennium when the aforementioned studies on ion hydration and ion distribution at the air−water interface contributed to rekindling interest in ion−solute interactions.38,39 Thus, the past decade has seen the development of powerful examples of solute(surface)−ion interaction models strongly supporting the notion that polarizable anions can interact with hydrophobic surfaces.40−47 Additionally, specific ion−solute interactions between polarizable anions and amide N−H and C(α)−H groups, and interactions between highly solvated anions such as sulfate and positively charged groups, have been recently pinpointed and quantified using peptide and poly amide models.41,48−51 Particularly of note in this regard is the similarity between both these types of interactions and those displayed by the C−F group of fluorinated molecules interacting with both N−H and C(α)−H groups and positively charged groups in
salt at the surface is lower than the bulk; but the concentration of iodide at the surface is higher than the bulk. Quod erat demonstrandum? A lack of molecular- or nanoscale details has also led to controversy in bulk solution. For example, from the earliest set of viscosity experiments studying the Hofmeister effect, the interpretation of the obtained data has been that ions affect the structure of bulk water, i.e., that the Hofmeister effect is dominated by ion−ion and ion−water interactions (Figure 1b).21−24 Furthermore, more recently, techniques including Raman IR,25 apparent water density,26 and neutron diffraction27 have also been interpreted in this way. With this perspective, salting-out salts have been referred to as water-structure makers or “kosmotropes” (Greek, n, kosmos, good order),5 while saltingin salts have been termed “chaotropes”28 (Greek, n, khaos vast chasm, more recently, disorder or confusion) or water-structure breakers. However, the idea that salts influence bulk water has been recently refuted by approaches that provide a more detailed view of the hydration of ions. Thus, techniques such as femtosecond time-resolved infrared spectroscopy (fs-IR),29−31 dielectric relaxation spectroscopy,29,32,33 optical Kerr-effect spectroscopy,32 and terahertz absorption spectroscopy34 have confirmed that, at least up to 1 M concentrations, salts do not influence the structure of water beyond the first or second solvation shell. 5625
DOI: 10.1021/acs.jpcb.5b01708 J. Phys. Chem. B 2015, 119, 5624−5638
Article
The Journal of Physical Chemistry B
ΔH° = 0.83 kcal mol−1, −TΔS° = −8.90 kcal mol−1 in the presence of NaClO4. In other words a highly exothermic binding process became an endothermic event because of competitive ClO4− binding to the pocket. It is important to note that this salt, and others that have binding anions, reduces the affinity of adamantane carboxylate (ΔΔG° = +1.20 kcal mol−1) for host 1 in accordance with the macroscale observation that these saltingin salts weaken the hydrophobic effect. These results therefore demonstrate that in this system the weakening of the hydrophobic effect arises because anion−hydrophobe (solute− salt) interactions can successfully compete with hydrophobe− hydrophobe (solute−solute) interactions. In this article, we detail the effect of salt concentration on the binding of four different organic guests to host 1. The results from these isothermal titration calorimetry (ITC) studies reveal a continuum of how the thermodynamic parameters of guest complexation are modulated by the concentration of salts; specifically, those with weakly solvated anions induce a decrease in affinity, those with strongly solvated anions show an increase, and those with intermediately solvated anions display both phenomena in a concentration-dependent manner.
proteins.52 Indeed, that a range of anions has affinity for amide and charged groups is in complete accord with anion affinity data from synthetic anions receptors, albeit that most of this data (∼80%) pertains to nonaqueous solutions.53,54 In contrast to the aforementioned studies of the interactions of ions with charged groups or polar hydrogen bond donors, little is known about specific, molecular level, interactions between anions and hydrophobic surfaces.42,43,55−57 Toward this, our own research has identified that polarizable anions have considerable affinity for hydrophobic concavity.58,59 We will discuss this further below, but it is clear that en masse the above results confirm that anions, particularly polarizable ones, can directly interact with solutes in water. Thus, in many cases it appears that there is no need to invoke the idea that, to pick a classic example, salts denature or precipitate proteins indirectly by perturbing water structure; they can do so by direct interactions with solutes. Nevertheless, there is still much to determine about ion−solute interactions in water, and how they, ion−water interactions, and other noncovalent interactions in the system fold together to generate the Hofmeister effect. While the study of proteins, polymers, and peptides have contributed to, and continue to contribute to, our understanding of the Hofmeister effect, the structural complicatedness of such species can make it difficult to parse out the different factors that lead to it. In contrast, replacing macromolecules with much more structurally straightforward molecules offers a means to circumnavigate this issue and reveal molecular-level factors contributing to the Hofmeister effect.60,61 Along this line of thought, we have previously shown that deep-cavity cavitand 1 (Figure 2) has an unusual affinity for weakly solvated anions, which can affect guest binding in a manner that follows the Hofmeister effect.58,59 Water-soluble host 162,63 (Figure 2) is a bowl-shaped amphiphile possessing an 8 Å wide × 8 Å deep hydrophobic pocket and a water-soluble outer surface decorated with eight carboxylic acids groups. Four of these are located on aromatic rings that are approximately perpendicular to the C4 axis of the host and form a hydrophobic rim around the portal of the pocket. This hydrophobic rim leads to a strong predisposition64 to dimerize in aqueous solution, and the resulting supramolecular nanocapsules have been shown to display a wide range of unusual phenomenon65,66 including physical and chemical (kinetic resolution) separations,67,68 and the ability to act as yoctoliter reaction vessels.69−75 While hydrophobic guests between the size of propane and steroids lead to dimerization,67,68,62 this is not the case with amphiphilic76−78 and anionic guests.58,59 Instead, because these polar guests increase the hydrophilicity of the rim and portal region of the host they turn off its predisposition to dimerization, and in such a quiescent state the host forms 1:1 complexes instead. The binding of anions to the hydrophobic pocket of 1 is testament to the power of concavity to bring about recognition. Under basic conditions (10 mM phosphate buffer, pH = 11.3) where the host can be expected79 to exist as a polyanion, ClO3−, I−, SCN−, and ClO4− have all been observed to bind to the hydrophobic concavity of the host;58,59 the strongest binder, ClO4−, binds to host 1 with an affinity of −2.67 kcal mol−1. The result of this binding to the hydrophobic pocket of 1 is that in excess a salt can effectively compete with a much more strongly binding organic guest.59 Thus, the thermodynamics of adamantane carboxylate binding to host 1 switches from ΔG° = −9.02 kcal mol−1, ΔH° = −8.97 kcal mol−1, −TΔS° = −46 cal mol−1 in the absence of added salt, to ΔG° = −7.80 kcal mol−1,
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EXPERIMENTAL SECTION Materials. Host 1 was synthesized according to the previously reported procedure.63 All inorganic salts and buffers, as well as guest molecules 2−5, were purchased from Aldrich Chemical Co. or Across and were used without further purification. Isothermal titration calorimetric data was gathered using a Microcal VP-ITC microcalorimeter regulated at 25 °C. Isothermal Titration Calorimetry (ITC) Protocols. Buffer solutions with the appropriate concentration of added salt were prepared by mixing 100 mM sodium phosphate buffer (pH 11.3) with either (1) stock salt solutions of 1 M concentration (or 0.5 M in the case of NaF) or (2) for solutions with final salt concentrations over 400 mM, the pure salt itself. The resulting solution was subsequently diluted to 10 mM phosphate of the desired salt concentration. The pH of each solution was monitored and kept at pH 11.3 ± 0.2 by the addition of small quantities of NaOH solution. It was only necessary to adjust the pH of the final solution at very high concentrations of salts, and in such cases, the addition of relatively small amounts of NaOH changed the total ionic strength negligibly (
Thermodynamic Profiles of Salt Effects on a Host−Guest System: New Insight into the Hofmeister Effect Corinne L. D. Gibb, Estelle E. Oertling, Santhosh Velaga, and Bruce C. Gibb* Department of Chemistry, Tulane University, New Orleans, Louisiana 70118, United States S Supporting Information *
ABSTRACT: Isothermal titration calorimetry was used to probe how salts influence the thermodynamics of binding of guests to cavitand 1. Studies involved six Hofmeister salts covering the range of salting-in to strongly salting-out. The latter were found to reduce affinity. The cause of this was competitive binding of the weakly solvated anion to the hydrophobic pocket of the host. At the other extreme of the Hofmeister series, salts increased guest affinity. Two factors for this were evident. At low concentrations the data fitted a previously reported model that accounts for cation condensation to the outer carboxylates of the host (Carnagie, R.; Gibb, C. L. D.; Gibb, B. C., Angew. Chem., Int. Ed. 2014, 53 (43), 11498−11500). At higher concentrations, an as of yet unidentified contribution was observed that was noted to be guest dependent. Midcontinuum salts such as NaClO3 were found to enhance affinity at low concentrations, but weaken it at high concentrations; a nonmonotonic trend attributed to the aforementioned competing phenomena. In combination with previous work, the data presented here reveal that the Hofmeister effect evident in this system can be mostly attributed to solute−salt interactions.
■
INTRODUCTION Aqueous solutions are ubiquitous in the biosphere, atmosphere, hydrosphere, and (at least)1 the palpable lithosphere, and consequently a thorough understanding of their properties is of importance to all sciences. A frequent observation in studies of the chemistry of aqueous solutions is the Hofmeister effect. Franz Hofmeister, in his landmark 1888 paper on the solubility of eggwhite proteins,2,3 noted that some salts decreased the solubility of proteins, whilst others did the opposite. In ordering the salts in terms of their precipitation power he formulated the first examples of what are now known as the Hofmeister series: one for cations and one for anions (Figure 1a).4 Subsequent to these initial studies, the Hofmeister series has been observed in at least 38 macroscopic phenomena pertaining to aqueous solutions.5−8 For example, if salts are ordered according to their ability to increase surface tension or increase (or decrease) surface potential very similar sequences are observed. However, despite being documented for over 125 years, there is as of yet no thorough explanation of the Hofmeister effect. At a most general level, for a three-component mixture of water, salt, and an organic co-solute there are six types of noncovalent interactions present in solution (Figure 1b), and it is the overall balance between these that controls the behavior and properties of the solution. Which noncovalent interactions dominate to engender the Hofmeister effect? The answer is likely system specific, depending on the nature of the salt and the structural features of the solute. However, even if this is the case there are likely yet to be determined semiquantitative guidelines © 2015 American Chemical Society
or quantitative models that will prove of utility in predicting or explaining properties of aqueous solutions. Historically, probing the Hofmeister effect has relied primarily on bulk-scale measurements. For example, at one of the simplest water interfaces, the air−water interface, early studies focused on surface tension and surface potential measurements for different concentrations of a range of salts.9,10 However, the lack of resolution of such studies, i.e., their inability to reveal what occurs at the molecular- or nanoscale, has led to controversy. For example, whereas the reactivity of aerosols dictates that certain anions must accumulate at the air−water interface,11−13 the measured increase in surface tension as a function of increasing salt concentration can only be accounted for by the Gibbs isotherm if there is a net depletion of ions from the interface.14 The actuality that dispelled this apparent contradiction was only relatively recently identified with a variety of empirical15−18 and computational studies6,19,20 identifying nonmonotonic concentration-profiles of ions at the air−water interface. For example, with sodium iodide it has been determined that iodide concentrations at the air−water interface are higher than the bulk but that there is a depletion layer underneath the immediate surface. In combination with a depletion layer of sodium ions at the air−water interface, but a higher than bulk concentration some 0.5 nm away from the interface, the net concentration of Received: February 19, 2015 Revised: April 2, 2015 Published: April 16, 2015 5624
DOI: 10.1021/acs.jpcb.5b01708 J. Phys. Chem. B 2015, 119, 5624−5638
Article
The Journal of Physical Chemistry B
Figure 1. (a) Typical Hofmeister series for anions and how they affect three representative physical properties. Length and direction of arrow correspond to the magnitude and direction of change, respectively. (b) Possible noncovalent interactions (blue lines) between components of an aqueous solution of a salt and a solute.
Figure 2. (a) Three representations of octa-acid host 1: chemical structure (left), space-filling model from the same perspective (center), and “plan” view looking down into the hydrophobic pocket (right). (b) To approximately the same scale, space-filling models of conjugate acids of, respectively, guests 2, 3, 4, and 5 (see main text).
Thus, while still undoubtedly playing a role in the Hofmeister effect, ion−water and ion−ion interactions apparently do not dominate. The possibility that other noncovalent interactions (Figure 1b) may be significant in the Hofmeister effect was explored in the 1960s and 1970, with, for example, the study of the interaction of lithium ions with amides groups,35,36 and the measurement of the thermodynamics of salt binding to polyacrylamide and polystyrene solid supports.37 Further studies on this topic were relatively infrequent, until around the turn of the millennium when the aforementioned studies on ion hydration and ion distribution at the air−water interface contributed to rekindling interest in ion−solute interactions.38,39 Thus, the past decade has seen the development of powerful examples of solute(surface)−ion interaction models strongly supporting the notion that polarizable anions can interact with hydrophobic surfaces.40−47 Additionally, specific ion−solute interactions between polarizable anions and amide N−H and C(α)−H groups, and interactions between highly solvated anions such as sulfate and positively charged groups, have been recently pinpointed and quantified using peptide and poly amide models.41,48−51 Particularly of note in this regard is the similarity between both these types of interactions and those displayed by the C−F group of fluorinated molecules interacting with both N−H and C(α)−H groups and positively charged groups in
salt at the surface is lower than the bulk; but the concentration of iodide at the surface is higher than the bulk. Quod erat demonstrandum? A lack of molecular- or nanoscale details has also led to controversy in bulk solution. For example, from the earliest set of viscosity experiments studying the Hofmeister effect, the interpretation of the obtained data has been that ions affect the structure of bulk water, i.e., that the Hofmeister effect is dominated by ion−ion and ion−water interactions (Figure 1b).21−24 Furthermore, more recently, techniques including Raman IR,25 apparent water density,26 and neutron diffraction27 have also been interpreted in this way. With this perspective, salting-out salts have been referred to as water-structure makers or “kosmotropes” (Greek, n, kosmos, good order),5 while saltingin salts have been termed “chaotropes”28 (Greek, n, khaos vast chasm, more recently, disorder or confusion) or water-structure breakers. However, the idea that salts influence bulk water has been recently refuted by approaches that provide a more detailed view of the hydration of ions. Thus, techniques such as femtosecond time-resolved infrared spectroscopy (fs-IR),29−31 dielectric relaxation spectroscopy,29,32,33 optical Kerr-effect spectroscopy,32 and terahertz absorption spectroscopy34 have confirmed that, at least up to 1 M concentrations, salts do not influence the structure of water beyond the first or second solvation shell. 5625
DOI: 10.1021/acs.jpcb.5b01708 J. Phys. Chem. B 2015, 119, 5624−5638
Article
The Journal of Physical Chemistry B
ΔH° = 0.83 kcal mol−1, −TΔS° = −8.90 kcal mol−1 in the presence of NaClO4. In other words a highly exothermic binding process became an endothermic event because of competitive ClO4− binding to the pocket. It is important to note that this salt, and others that have binding anions, reduces the affinity of adamantane carboxylate (ΔΔG° = +1.20 kcal mol−1) for host 1 in accordance with the macroscale observation that these saltingin salts weaken the hydrophobic effect. These results therefore demonstrate that in this system the weakening of the hydrophobic effect arises because anion−hydrophobe (solute− salt) interactions can successfully compete with hydrophobe− hydrophobe (solute−solute) interactions. In this article, we detail the effect of salt concentration on the binding of four different organic guests to host 1. The results from these isothermal titration calorimetry (ITC) studies reveal a continuum of how the thermodynamic parameters of guest complexation are modulated by the concentration of salts; specifically, those with weakly solvated anions induce a decrease in affinity, those with strongly solvated anions show an increase, and those with intermediately solvated anions display both phenomena in a concentration-dependent manner.
proteins.52 Indeed, that a range of anions has affinity for amide and charged groups is in complete accord with anion affinity data from synthetic anions receptors, albeit that most of this data (∼80%) pertains to nonaqueous solutions.53,54 In contrast to the aforementioned studies of the interactions of ions with charged groups or polar hydrogen bond donors, little is known about specific, molecular level, interactions between anions and hydrophobic surfaces.42,43,55−57 Toward this, our own research has identified that polarizable anions have considerable affinity for hydrophobic concavity.58,59 We will discuss this further below, but it is clear that en masse the above results confirm that anions, particularly polarizable ones, can directly interact with solutes in water. Thus, in many cases it appears that there is no need to invoke the idea that, to pick a classic example, salts denature or precipitate proteins indirectly by perturbing water structure; they can do so by direct interactions with solutes. Nevertheless, there is still much to determine about ion−solute interactions in water, and how they, ion−water interactions, and other noncovalent interactions in the system fold together to generate the Hofmeister effect. While the study of proteins, polymers, and peptides have contributed to, and continue to contribute to, our understanding of the Hofmeister effect, the structural complicatedness of such species can make it difficult to parse out the different factors that lead to it. In contrast, replacing macromolecules with much more structurally straightforward molecules offers a means to circumnavigate this issue and reveal molecular-level factors contributing to the Hofmeister effect.60,61 Along this line of thought, we have previously shown that deep-cavity cavitand 1 (Figure 2) has an unusual affinity for weakly solvated anions, which can affect guest binding in a manner that follows the Hofmeister effect.58,59 Water-soluble host 162,63 (Figure 2) is a bowl-shaped amphiphile possessing an 8 Å wide × 8 Å deep hydrophobic pocket and a water-soluble outer surface decorated with eight carboxylic acids groups. Four of these are located on aromatic rings that are approximately perpendicular to the C4 axis of the host and form a hydrophobic rim around the portal of the pocket. This hydrophobic rim leads to a strong predisposition64 to dimerize in aqueous solution, and the resulting supramolecular nanocapsules have been shown to display a wide range of unusual phenomenon65,66 including physical and chemical (kinetic resolution) separations,67,68 and the ability to act as yoctoliter reaction vessels.69−75 While hydrophobic guests between the size of propane and steroids lead to dimerization,67,68,62 this is not the case with amphiphilic76−78 and anionic guests.58,59 Instead, because these polar guests increase the hydrophilicity of the rim and portal region of the host they turn off its predisposition to dimerization, and in such a quiescent state the host forms 1:1 complexes instead. The binding of anions to the hydrophobic pocket of 1 is testament to the power of concavity to bring about recognition. Under basic conditions (10 mM phosphate buffer, pH = 11.3) where the host can be expected79 to exist as a polyanion, ClO3−, I−, SCN−, and ClO4− have all been observed to bind to the hydrophobic concavity of the host;58,59 the strongest binder, ClO4−, binds to host 1 with an affinity of −2.67 kcal mol−1. The result of this binding to the hydrophobic pocket of 1 is that in excess a salt can effectively compete with a much more strongly binding organic guest.59 Thus, the thermodynamics of adamantane carboxylate binding to host 1 switches from ΔG° = −9.02 kcal mol−1, ΔH° = −8.97 kcal mol−1, −TΔS° = −46 cal mol−1 in the absence of added salt, to ΔG° = −7.80 kcal mol−1,
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EXPERIMENTAL SECTION Materials. Host 1 was synthesized according to the previously reported procedure.63 All inorganic salts and buffers, as well as guest molecules 2−5, were purchased from Aldrich Chemical Co. or Across and were used without further purification. Isothermal titration calorimetric data was gathered using a Microcal VP-ITC microcalorimeter regulated at 25 °C. Isothermal Titration Calorimetry (ITC) Protocols. Buffer solutions with the appropriate concentration of added salt were prepared by mixing 100 mM sodium phosphate buffer (pH 11.3) with either (1) stock salt solutions of 1 M concentration (or 0.5 M in the case of NaF) or (2) for solutions with final salt concentrations over 400 mM, the pure salt itself. The resulting solution was subsequently diluted to 10 mM phosphate of the desired salt concentration. The pH of each solution was monitored and kept at pH 11.3 ± 0.2 by the addition of small quantities of NaOH solution. It was only necessary to adjust the pH of the final solution at very high concentrations of salts, and in such cases, the addition of relatively small amounts of NaOH changed the total ionic strength negligibly (
