Transport Properties of Carbohydrates: Towards the Minimization Toxicological Risks of Cobalt and Chromium Ions

: The inﬂuence of oligosaccharides ( α -cyclodextrin, β -cyclodextrin and γ -cyclodextrin), and a polysaccharide, sodium hyaluronate (NaHy), on the diffusion of aqueous solutions of cobalt and chromium chlorides has been investigated. Cobalt and chromium are constituents of metal alloys for biomedical use, including dental prostheses. Thus, the release of these ions in the human body can lead to harmful biological effects. The interaction of metal ions with saccharides might have information on the role of mouthwashes in preventing these effects. This interaction has been assessed by measuring multicomponent intermolecular diffusion coefﬁcients at 298.15 K. It has been found that β -cyclodextrin has the highest interaction towards cobalt and chromium ions. This work will contribute to unveiling the mechanisms responsible for transport by diffusion in aqueous solutions, and, therefore, mitigating the potential toxicity inherent to those metal ions.


Introduction
The toxicity of heavy metals is an issue of growing concern in the scientific community. Although some of these metals such as cobalt (Co) and chromium (Cr) are essential nutrients, used in various biochemical and physiological functions [1] at high doses, regardless of their different oxidation states, they exhibit high toxicity [2].
Heavy metal-induced toxicity and carcinogenicity involve many mechanistic aspects, some of which are not clearly elucidated [1,3]. Human exposure to cobalt and chromium can occur for a short time or by prolonged exposure through inhalation, ingestion, or skin contact [4,5]. In human primary cells and experimental systems, cobalt metal seems to induce oxidative stress, chronic inflammation, changes in cell proliferation and death [6]; cobalt metal has also recently been classified as a C1B, M2, and R1B substance by the EU REACH Regulation, which has a significant and a direct impact on the application of Co-Cr biomedical alloys [7,8], despite the fact that metal cobalt presents physicochemical properties different from Co-based biomedical alloys [9].
It also should be stressed that chromium in its +6 oxidation state is also classified as human carcinogenic by the International Agency for Research on Cancer (IARC) [10]. It Table 1 describes all the reagents used as received in the present work, including cobalt chloride, chromium chloride, α-cyclodextrin, β-cyclodextrin and γ-cyclodextrin, and sodium hyaluronate. All chemicals were used without further purification.
All solutions were prepared using ultrapure water (Millipore, Germany, Milli-Q Advantage A10, specific resistance = 1.82 × 105 Ω m, at 298.15 K). The weighing was performed using a Radwag AS 220C2 balance (Radwag, Radom, Poland), with an accuracy of ±0.0001 g. The concentrations of cyclodextrins were computed by correcting their water content.  1 Values provided by the suppliers. 2 In this work, we used two samples of NaHy with different molecular weights (i.e., Mw = 124 kDa and 243 kDa). 3 β-Cyclodextrin with water mass fraction 0.131.

pH Measurements
The pH values were obtained using a Radiometer PHM 240 pH meter (Radiometer, Copenhagen, Denmark) coupled to a pH conjugate electrode (Ingold U457-K7). The pH measurements were obtained in recently prepared solutions, at 298.15 K, and after previous calibration of the electrode using, for this purpose, pH 4, 7 and 10 buffer solutions. The measurement sensitivity was greater than 98.7% and zero pH was equal to 6.11 ± 0.03.

Taylor Dispersion Technique
The Taylor diffusion technique allows the measurement of diffusion coefficients in multicomponent systems and, as the name implies, is based on the work carried out by G.I. Taylor in the 1950s of the last century, being profusely described in the literature [36][37][38][39]. A summary of the most relevant issues related to the technique will be described in the following section. As a common feature of all chromatographic-based techniques, a disperse profile is obtained by injecting a volume equal to 0.063 mL of solution, at the beginning of the experiment, into a Teflon tube with a length and internal diameter of 3048.0 (±0.1) cm and 0.06440 ± (0.00006) cm, respectively, where a solution of defined concentration and composition flows in laminar flow. All equipment is thermostated at a temperature of 298.15 (±0.01) K. The dispersion obtained in the sequence of different flows, of the different species, is registered using a differential refractometer (Waters model 2410). This equipment measures the electric potential as a function of time, V(t), by coupling a digital voltmeter (Agilent 34401 A).
In Equation (1), V max is the dispersion peak height, V 0 and V 1 are the baseline voltage and baseline slope, respectively, W 1 is the normalized pre-exponential factor, D 1 and D 2 are the eigenvalues of the ternary diffusion coefficient matrix, r is the internal radius of the dispersion tube and t R is the mean sample retention time.
The values of the tracer diffusion coefficients, D T , for NaHy in aqueous solutions of cobalt chloride and chromium chloride were also measured. For these pseudo-binary systems, CoCl 2 (1)/NaHy(2) and CrCl 3 (1)/NaHy(2), the previous dispersion equation (Equation (1)) can be simplified, and can be described as In fact, these systems can be considered as pseudo-binary, considering that the concentration of the salt under study (component 1) is significantly higher than the concentration of NaHy (component 2), ensuring the occurrence of tracer diffusion of the latter and the concentrations of CoCl 2 (or CrCl 3 ) in the injection and carrier solutions can be assumed as equal.
More details on how the binary and ternary diffusion coefficients can be calculated can be found in the following references [43][44][45].

Results
pH measurements were taken for the solutions containing cobalt chloride and chromium chloride, at 0.010 M, without and with cyclodextrins (α-CD, β-CD or γ-CD) or NaHy, to assess the state of metal ion species (Table 2). It can be observed that for the Co(II)containing solutions, the pH is lower than ca. 6 and for Cr(III), the solutions have a pH lower than 4. At these pH values, we can say that the cobalt ion species are essentially in a non-hydrolyzed form [46]. Concerning the Cr 3+ ions, the presence of hydrolyzed species cannot be ruled out. Tables 3 and 4 summarize the mean values of the D ik diffusion coefficients for the solutions of different compositions and concentrations for six aqueous systems, involving two salts (CoCl 2 and CrCl 3 ) and three cyclodextrins (α-CD, β-CD and γ-CD). The values were calculated by fitting Equation (1) to dispersion curves; the number of replicas is always greater than four. The main diffusion coefficients (D 11 and D 22 ) have an uncertainty value smaller than (±0.015 × 10 −9 m 2 s −1 ), whilst the cross-diffusion coefficients (D 12 and D 21 ) have an uncertainty value smaller than (±0.030 × 10 −9 m 2 s −1 ).
At the limiting situations of X 1 = 0 and X 1 = 1, the values of D 11 correspond to the tracer diffusion coefficient of CoCl 2 (or CrCl 3 ) in CDs and the binary mutual diffusion coefficient of aqueous CoCl 2 (or CrCl 3 ) at 0.001 and 0.01 M, respectively. Regarding these latter values for D 11 , a good agreement is observed between them and the binary diffusion coefficient values reported in previous works [47,48]. For example, for aqueous CrCl 3 solutions at 0.01 M, the deviations are equal to or less than 0.8% between the binary value D = 1.170 × 10 −9 m 2 s −1 [47] and the D 11 values shown in Table 3 (D 11 = 1.172 × 10 −9 m 2 s −1 , D 11 = 1.180 × 10 −9 m 2 s −1 and D 11 = 1.160 × 10 −9 m 2 s −1 ). Table 3. Ternary diffusion coefficients (D 11 , D 12 , D 21 , D 22 1 of aqueous CrCl 3 (C 1 ) + CDs (C 2 ) solutions.  Table 4. Ternary diffusion coefficients (D 11 , D 12 , D 21 , D 22 ) 1 of aqueous CoCl 2 (C 1 ) + CDs (C 2 ) solutions.  Tables 5 and 6 show the average values of the binary and ternary diffusion coefficients of NaHy in different aqueous solutions containing CoCl 2 (or CrCl 3 ) at the following two different concentrations: 0.001 and 0.010 M. These values were calculated from, at least, six independent measurements. Once the high viscosity of sodium hyaluronate strongly affects the measurement of the diffusion coefficients, these measurements were only carried out at tracer concentrations (Section 2.2.2). While the main diffusion coefficients D 11 and D 22 were generally reproducible within ± (0.020 × 10 −9 m 2 s −1 ), the cross-coefficients were in general reproducible within about ± (0.040 × 10 −9 m 2 s −1 ).
From Table 6, we can observe that whereas the limiting values for cross-coefficients D 21 at the infinitesimal concentration are practically zero, within the experimental error, the cross-coefficients D 12 differ from zero. In the other words, D 12 < 0 indicates that the gradient in the concentration of NaHy produces counter-current coupled flows of CoCl 2 and CrCl 3 . Table 5. Tracer diffusion coefficients, app D 0 T , for NaHy 1 in aqueous solutions of CoCl 2 and CrCl 3 at 0.001 and 0.010 M, and T = 298.15 K.

Discussion
From Tables 2 and 3, it can be observed that the limiting values for the infinitesimal concentration of cross-coefficients D 21 can be considered null, taking into account the experimental error. This arises, most probably, due to the similarity of the mobilities of CD free species and eventual aggregates of CoCl 2 (or CrCl 3 ) and CDs. However, D 12 < 0; that is, the gradient in the concentration of CD (α-CD, β-CD and γ-CD) produces counter-current coupled flows of these salts, which are the most significant in highly concentrated solutions of β-CD. These observations can readily be explained by the following two phenomena: the hydrolysis of cobalt and chromium ions and association between CoCl 2 (or CrCl 3 ) and these cyclodextrin molecules, leading to the formation of complexes in solution. This phenomenon will lead to a decrease in free cobalt (or chromium ions), and, consequently, to compensate for that loss, a counterflow of these salts will occur.
In fact, the diffusion of these salts can be affected by Co(II) and Cr(III) hydrolysis. As cobalt chloride and chromium chloride aqueous solutions are acidic if unbuffered (Table 2), when these salts diffuse in water, the hydronium ions produced by hydrolysis of the cobalt and chromium ions (as shown in Equations (3) and (4)) should diffuse ahead of the lessmobile cobalt (or chromium ions), producing a counter flow of chloride acid in addition to the main flow of partially hydrolyzed cobalt chloride (or chromium chloride) [47][48][49].
In other words, once the H3O + ion has much higher mobility than Clfrom the anomalous mechanism for H + proton transport in water, a strong electric field is generated, slowing down the H3O + ions driving the large counter-current fluxes of Cr(III) (or Co(II)) species, free or associated with CD molecules and, thus, D12 < 0. Despite the diffusion of aqueous cobalt chloride (or chromium chloride) being a ternary process because there is a small but additional flow of chloride acid, we can consider that if corrections for chloride acid diffusion are not made, the apparent binary diffusion coefficients of CoCl2 (or CrCl3) can only be 1-3%, which is too large. Support for this observation is given in the literature where the negligible effect of the hydrolysis of the beryllium ion on the diffusion of BeSO4 In other words, once the H3O + ion has much higher mobility than Clfrom the anomalous mechanism for H + proton transport in water, a strong electric field is generated, slowing down the H3O + ions driving the large counter-current fluxes of Cr(III) (or Co(II)) species, free or associated with CD molecules and, thus, D12 < 0. Despite the diffusion of aqueous cobalt chloride (or chromium chloride) being a ternary process because there is a small but additional flow of chloride acid, we can consider that if corrections for chloride In other words, once the H 3 O + ion has much higher mobility than Cl − from the anomalous mechanism for H + proton transport in water, a strong electric field is generated, slowing down the H 3 O + ions driving the large counter-current fluxes of Cr(III) (or Co(II)) species, free or associated with CD molecules and, thus, D 12 < 0. Despite the diffusion of aqueous cobalt chloride (or chromium chloride) being a ternary process because there is a small but additional flow of chloride acid, we can consider that if corrections for chloride acid diffusion are not made, the apparent binary diffusion coefficients of CoCl 2 (or CrCl 3 ) can only be 1-3%, which is too large. Support for this observation is given in the literature where the negligible effect of the hydrolysis of the beryllium ion on the diffusion of BeSO 4 is analyzed [50].
However, for aqueous systems containing CoCl 2 (or CrCl 3 ) plus β-CD, the D 12 values are significantly more negative when compared with those obtained for the systems containing α-CD and γ-CD. The formation of aggregates between Co 2+ and Cr 3+ ions, and β-CD molecules can be other phenomenon that also occur, therefore justifying this difference in thermodynamic behavior between them.
Assuming the formation of a 1:1 supramolecular complex between these cations (Co 2+ and Cr 3+ ) and β-CD (Equations (5) and (6)), and considering the values indicated in Table 7 for the limiting diffusion coefficients of the free and complexed species, the values for these binding constants K (Equations (7) and (8)) can be computed [45] and are equal to In other words, once the H3O + ion has much higher mobility than Clfrom the anomalous mechanism for H + proton transport in water, a strong electric field is generated, slowing down the H3O + ions driving the large counter-current fluxes of Cr(III) (or Co(II)) species, free or associated with CD molecules and, thus, D12 < 0. Despite the diffusion of aqueous cobalt chloride (or chromium chloride) being a ternary process because there is a small but additional flow of chloride acid, we can consider that if corrections for chloride acid diffusion are not made, the apparent binary diffusion coefficients of CoCl2 (or CrCl3) can only be 1-3%, which is too large. Support for this observation is given in the literature where the negligible effect of the hydrolysis of the beryllium ion on the diffusion of BeSO4 is analyzed [50].
However, for aqueous systems containing CoCl2 (or CrCl3) plus β-CD, the D12 values are significantly more negative when compared with those obtained for the systems containing α-CD and γ-CD. The formation of aggregates between Co 2+ and Cr 3+ ions, and β-CD molecules can be other phenomenon that also occur, therefore justifying this difference in thermodynamic behavior between them.
Assuming the formation of a 1:1 supramolecular complex between these cations (Co 2+ and Cr 3+ ) and β-CD (Equations (5) and (6)), and considering the values indicated in Table  7 for the limiting diffusion coefficients of the free and complexed species, the values for these binding constants K (Equations (7) and (8)) can be computed [45] and are equal to 40 (±0.9) M −1 and 30 (±0.6) M −1 .

Species
Ds/(10 −9 m 2 s −1 ) In other words, once the H3O + ion has much higher mobility than Clfrom the anomalous mechanism for H + proton transport in water, a strong electric field is generated, slowing down the H3O + ions driving the large counter-current fluxes of Cr(III) (or Co(II)) species, free or associated with CD molecules and, thus, D12 < 0. Despite the diffusion of aqueous cobalt chloride (or chromium chloride) being a ternary process because there is a small but additional flow of chloride acid, we can consider that if corrections for chloride acid diffusion are not made, the apparent binary diffusion coefficients of CoCl2 (or CrCl3) can only be 1-3%, which is too large. Support for this observation is given in the literature where the negligible effect of the hydrolysis of the beryllium ion on the diffusion of BeSO4 is analyzed [50].
However, for aqueous systems containing CoCl2 (or CrCl3) plus β-CD, the D12 values are significantly more negative when compared with those obtained for the systems containing α-CD and γ-CD. The formation of aggregates between Co 2+ and Cr 3+ ions, and β-CD molecules can be other phenomenon that also occur, therefore justifying this difference in thermodynamic behavior between them.
Assuming the formation of a 1:1 supramolecular complex between these cations (Co 2+ and Cr 3+ ) and β-CD (Equations (5) and (6)), and considering the values indicated in Table  7 for the limiting diffusion coefficients of the free and complexed species, the values for these binding constants K (Equations (7) and (8)) can be computed [45] and are equal to 40 (±0.9) M −1 and 30 (±0.6) M −1 .
Cr 3+ (aq) + β-CD(aq) ⇆ Cr 3+ − β-CD (aq) = . β = β (8)  From the values of these constants, we can consider that this interaction between these species is not negligible, and thus, some amounts of Co(II) (or Cr(III)) and β-CD molecules can be transported as Co 2+ -β-CD (or Cr 3+ -β-CD) complexes. In the range of higher β-CD concentrations, a high percentage of chromium chloride (or cobalt chloride) is in complexed form (i.e., associated with cyclodextrin). Consequently, the β-CD concentration gradient is responsible for a gradient in the opposite direction for the concentration of chromium (or cobalt) cations. This justifies the occurrence of a countercurrent to the main flow of chromium chloride and, consequently, the D 12 values are negative for these solutions at the molar faction of salt X 1 = 1 (Tables 2 and 3).
In relation to other CDs, at which D 12 ≈ 0, the interaction with these metal ions might be considered negligible. One possible explanation for the anomalous and unexpected diffusion behavior of β-CD in the presence of these salts may be attributed to its peculiar, less flexible molecular structure [52] and to the reduced number of hydroxyl groups capable of establishing hydrogen bonds with surrounding water molecules, as a consequence of the intramolecular hydrogen bonds between their secondary hydroxyl groups (that is, between a hydroxyl group at C-2 and a glucose unit and a hydroxyl group at C-2 of another adjacent glucose unit [53]). The presence of ions Co 2+ and Cr 3+ in these solutions will perturb the dynamic structure of the water molecules surrounding β-CD and the intra cavity water molecules, as a consequence of the strong electrostatic interactions between their available hydroxyl groups and these ions, leading to the formation of complexes in solution, which are expected to demonstrate lower mobility than free species. Support for this observation is pointed out by Coleman et al. [54], and Poulson et al. [55] when they verified that multivalent cations lead to a significant alteration in β-cyclodextrin solubility, in aqueous solutions. This evidence demonstrates that this phenomenon is a result of the modification of the structure of water and leads to more favorable interactions with the β-CD supramolecular complexes.
Relative to the effect of the presence of NaHy on the diffusion behavior of CoCl 2 (or CrCl 3 ), we can say that this carbohydrate also significantly affects this parameter, as shown by the D 12 < 0 values. (Table 6). This fact is not unexpected, bearing in mind the different mobilities of the sodium cation and the hyaluronate anions; that is, λ 0 (Na + ) = 50.10 × 10 −4 Ω −1 m 2 mol −1 and λ 0 (Hy − monomer) = 40.05 × 10 −4 Ω −1 m 2 mol −1 ) [56]. Once the Na + ion has much higher mobility than Hy − , when there is a gradient of NaHy in solution, a strong electric field is generated, slowing down the Na + ions and driving large counter-current fluxes of Cr 3+ (or Co 2+ ) species, free or associated and D 12 < 0.
Information about coupled diffusion can be also inferred by the calculated values of the ratio D 12 /D 22 (Table 8). The higher negative ratio values for CoCl 2 /NaHy and CrCl 3 /NaHy systems, when compared with others, permits us to conclude that one mole of diffusing NaHy counter-transports up to 2 mol of CoCl 2 (or up to 1.2 mol of CrCl 3 ). Table 8. Estimation of the moles of CoCl 2 and CrCl 3 transported for each mol of α-CD, β-CD, γ-CD, and NaHy 0.1%, obtained from D ij data shown in Tables 2 and 3.

Conclusions
Sodium hyaluronate and one of the studied cyclodextrins, β-cyclodextrins, present a greater interaction with cobalt and chromium ions, which is why we consider them to be the best carrier agents for these metal ions. D 12 negative and K (40 (±0.9) M −1 and 30 (±0.6) M −1 ) values show that β-CD interacts with both cobalt and chromium ions. This complexation prevents the occurrence of the hydrolysis of metal ions. It can be concluded that the interaction of ions with only β-CD probably arises from the perturbation of the structure of water and leads to less unfavorable interactions with the β-CD aggregates.
The present work shows that cyclodextrins and hyaluronic acid interact with cobalt and chromium ions once a significant amount of these salts per each mol of these carbohydrates (at most 2 mol of CoCl 2 per mol of NaHy) is transported. It can be hypothesized that the presence of these carbohydrates into mouthwash formulation might mitigate the toxicity inherent to the presence of metal ions.
We believe that the data obtained can be of great value to the entire scientific and technological community that works with these metals.  Data Availability Statement: All data are presented in this paper.

Conflicts of Interest:
The authors declare no conflict of interest.