# Investigation of an Organogel by Micro-Differential Scanning Calorimetry: Quantitative Relationship between the Shapes of the Thermograms and the Phase Diagram

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## Abstract

**:**

## 1. Introduction

## 2. Results and Discussion

#### 2.1. Aspect of the Thermograms

#### 2.2. Measurements of the Molar Enthalpies

_{s}is the number of moles of gelators transitioning from the solid state to the liquid phase, opposite to $d{n}_{\mathrm{l}}$, the increment in the number of moles appearing in the liquid phase. If the heat flow is integrated between a temperature ${T}_{1}$ (chosen as low as possible) and a temperature T, the corresponding enthalpy is:

_{s}in the solid phase can be calculated and hence the quantity ∆H/n (Equation (4)).

#### 2.3. Measurement of Transition Temperatures

#### 2.4. Calculation of the Soluble Fraction of Gelator from the Thermograms

#### 2.5. Comparison of the Endotherms with the Exotherms

## 3. Conclusions

## 4. Materials and Methods

#### 4.1. Materials

#### 4.2. Micro-Differential Scanning Calorimetry

#### 4.3. Correction of the Heat Flows

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**DSC thermograms of HSA/nitrobenzene gels for various weight fractions W from 0.0025 to 0.04 in HAS (endo up). Heating rate 0.1 °C/min. The curves were normalized to the masses m of the gelator HSA and staggered for clarity.

**Figure 2.**Apparent molar enthalpies as a function of weight concentration. The enthalpies ∆H are calculated by integrating the heat flows from 14 °C to a temperature above the complete melting of the gel. They are divided by n, the number of moles of gelator in the sample. Dashed line fit of the data with Equation (4) corresponding to the lever rule. The optimal parameters of the fit are ${w}_{l,1}$ = 0.00067 (solubility at 14 °C in wt % fraction); L = 62.7 kJ/mol (molar melting enthalpy).

**Figure 3.**Schematic phase diagram, with the definition of the quantities used in equations. ${T}_{\mathrm{m}}$ is the temperature where all the gelator is solubilized. ${w}_{\mathrm{l}}$ is the weight fraction of the gelator in the liquid phase. Above ${T}_{\mathrm{m}}$, ${w}_{\mathrm{l}}\left(T\right)=W$. ${T}_{1}$ is the lower limit integration of the heat flow to calculate the enthalpy ∆H. The red part of the liquidus and the arrow indicate the evolution of the gelator fraction in the liquid phase when T increases.

**Figure 4.**(

**a**) Different measured temperatures on a thermogram (e.g., weight fraction W = 0.0025). Red: heat flow; blue: integral of the heat flow $\u2206{H}_{1}^{T}$. ${T}_{\mathrm{max}}$ is the temperature at the maximum of the endotherm, ${T}_{\mathrm{end}}$, at the end of the peak. The gap between both temperatures is about 12 °C. Two other temperatures measured on thermograms are the inflection point and the temperature by the tangent method [21]. The integral method measures the temperature at the intersection of the plateau and the tangent of the ascending branch at ${T}_{\mathrm{max}}$. Note that ${T}_{\mathrm{GS}}$ measured by rheology in this case is 34.7 °C. (

**b**) Superimposition of the different T values with the c-T phase diagram of HSA/nitrobenzene measured by NMR, rheology, DSC, by us and others (Christ et al.: Ref. [19]; Terech: Ref. [12]). The errors of ${T}_{\mathrm{max}}$ and ${T}_{\mathrm{infl}}$ are 0.2 °C; the errors of ${T}_{\mathrm{end}}$ and T measured by the integral method are 0.5 °C. For DSC experiments, the uncertainties of the weight fractions W are less than 2.9%.

**Figure 5.**Thermograms normalized to the total mass of gel. (

**a**) Raw data. (

**b**) Thermograms corrected from the heat capacity differences of the cell as described in Materials and Methods. The ascending parts of the curves before transition temperatures ${T}_{\mathrm{m}}$ are superimposed.

**Figure 6.**Thermogram of HSA/nitrobenzene (0.03 wt. fraction). Integration of the heat flow after subtraction of two different baselines. The straight baseline is the one subtracted from the commercial software. The other baseline is $r{W}_{\mathrm{l}}\u2206{C}_{\mathrm{p}}$ (${W}_{\mathrm{l}}$ calculated from Equation (8) and normalized to match the value of the plateau after the transition ≈$\mathrm{W}\u2206{C}_{\mathrm{p}}$ and multiplied by the heating rate r to convert the quantity to heat flow).

**Figure 7.**Derivation of the weight fractions ${w}_{\mathrm{l}}\left(T\right)$ of HSA in the liquid phase from the integrals of the thermograms from Equations (5) and (6) and their superimposition with the phase diagram. (

**a**) Linear representation; (

**b**) logarithm representation. The different points are those of the phase diagram (Figure 4b, with switched axes) with the same legend. For clarity, errors bars have been represented only for three samples (0.0015, 0.0075, and 0.04) and every 400 points.

**Figure 8.**(

**a**) Comparison of the heat flow during heating (red) and cooling (blue); W = 0.03. One of the thermograms is multiplied by −1 to make both flows positive and compare them. (

**b**) Weight fractions of the gelator in the liquid phase derived from both heat flows with Equations (6) and (8). On cooling, the plateau crosses the liquidus, indicating a supersaturated solution. The drop in concentration indicates the solidification of the gelator.

**Figure 9.**Variation of the gap $\delta \left({T}_{1}\right)$ with W and measurement of constant $K\left({T}_{1}\right)$.

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**MDPI and ACS Style**

Schwaller, D.; Christ, E.; Legros, M.; Collin, D.; Mésini, P.J. Investigation of an Organogel by Micro-Differential Scanning Calorimetry: Quantitative Relationship between the Shapes of the Thermograms and the Phase Diagram. *Gels* **2021**, *7*, 93.
https://doi.org/10.3390/gels7030093

**AMA Style**

Schwaller D, Christ E, Legros M, Collin D, Mésini PJ. Investigation of an Organogel by Micro-Differential Scanning Calorimetry: Quantitative Relationship between the Shapes of the Thermograms and the Phase Diagram. *Gels*. 2021; 7(3):93.
https://doi.org/10.3390/gels7030093

**Chicago/Turabian Style**

Schwaller, Duncan, Elliot Christ, Mélanie Legros, Dominique Collin, and Philippe J. Mésini. 2021. "Investigation of an Organogel by Micro-Differential Scanning Calorimetry: Quantitative Relationship between the Shapes of the Thermograms and the Phase Diagram" *Gels* 7, no. 3: 93.
https://doi.org/10.3390/gels7030093