# Relation in Alginate-Based Magnetic Suspensions
## 3 Results
In the case of composite formation, these steps are based on the dissolution of polymer and composite in a good solvent. Then, water taken as a good solvent for Na-alginate and its composites, the steps of the thermodynamic cycle which corresponds to Equation (2) are:  
\[\text{Na-alginate polymer + water = Solution + }\Delta H_{1} \tag{3}\]  
\[\text{Solid MNPs + water = Suspension 1 + }\Delta H_{2} \tag{4}\]  
\[\text{Solution + Suspension 1 = Suspension 2 + }\Delta H_{3} \tag{5}\]  
\[\text{Composite + water = Suspension 2 + }\Delta H_{4} \tag{6}\]  
All these steps can be performed in a calorimeter and the resulting combination of the enthalpy values reads:  
\[\Delta H_{adh}=\Delta H_{1}+\Delta H_{2}+\Delta H_{3}-\Delta H_{4} \tag{7}\]  
It is worthwhile noting that values \(\Delta H_{1}\) and \(\Delta H_{2}\) relate to individual components but the value \(\Delta H_{4}\) for the dissolution of a composite is a function of the polymer content in it. Typically, the value \(\Delta H_{3}\) related to the mixing of a solution with a suspension of MPs (Equation (5)) is small, it falls within the limits of the experimental error for the other values in the cycle, and it is usually neglected. Composites based on Na-alginate polymer with embedded MPs in different content were prepared separately as described above in the Materials and Methods part. Figure 7 presents the concentration dependence of the enthalpy of dissolution (\(\Delta H_{4}\)) of these composites in water at 25 \({}^{\circ}\)C measured in a direct experiment in calorimeter. Ni and Ni@C MPs were taken as examples. Figure 7 contains all the necessary information to calculate the enthalpy of adhesion using the thermodynamic cycle in Equation (7). The value at the left-side ordinate axis corresponds to the composite with 0% content of MPs, which is pure Na-alginate. It is the \(\Delta H_{1}\) value in Equation (3). The value at the right-side axis is \(\Delta H_{2}\) in Equation (4) as it corresponds to the composite with 100% of MPs. Other points in the plot correspond to the values of the enthalpy of dissolution of composites with progressively increasing MPs content (\(\Delta H_{4}\) in Equation (6)). In fact, any composite is a mixture of components and even if there is no interaction between components, the enthalpy of dissolution would depend on the proportion of the components in a mixture as the values of \(\Delta H_{1}\) and \(\Delta H_{2}\) are different. Theoretically, the enthalpy of dissolution of an additive mixture of components would be a linear function between the values for the constituents. It is noticeable in Figure 7 that it was the case of Na-alginate composites with embedded Ni MPs. The experimental points for the enthalpy of dissolution in this system are close to a straight line between \(\Delta H_{1}\) and \(\Delta H_{2}\). Meanwhile, the values of the enthalpy of dissolution for Na-alginate composites with Ni@C deviated upward from the straight line of an additive mixture. It meant that there was the interaction between components in composites with Ni@C particles, unlike the system with Ni MPs. Most likely it was the result of the surface modification of Ni with a carbon layer. Experimental data presented in Figure 7 and similar data for Na-alginate composites with Fe\({}_{3}\)O\({}_{4}\) and Fe MPs were used for the calculation of the enthalpy of adhesion of Na-alginate to the surface of MPs using Equation (7). The results are plotted in Figure 8, which gives concentration dependence on the enthalpy of adhesion. The values of the enthalpy of adhesion are related to the unit area (m\({}^{2}\)) of the surface of the embedded MPs. Figure 4:0 Enthalpy of dissolution of Na-alginate + MPs composites in water (\(\Delta H_{4}\)) at 25 \({}^{\circ}\)C. Values at the ordinate axes correspond to the enthalpy of dissolution of Na-alginate (left axis—\(\Delta H_{1}\)) and to the enthalpy of wetting of MNPs (right axis—\(\Delta H_{2}\)). Experimental data for Ni and Ni@C are presented.