3.5.3. Frequency Sweep

Frequency sweep tests were performed on the starch gels formed in situ after the temperature sweep. The G and G- of the samples were dependent on the oscillation frequency, indicating a typical viscoelastic nature of the starch gels [42] (Figure 3E,F). G- and G- increased as the frequency increased; therefore, the overall chain mobility within the network was relatively high. G was higher than G- at the same angular frequency throughout the entire tested angular frequency range (0.1 to 100 rad/s), indicating that these starch gels exhibited dominant elastic behavior compared to viscous behavior [45]. The power-law fitting parameters affected by the frequency are shown in Table 3. The power law model represents the experimental data of G and G- since the determination coefficients (R-<sup>2</sup> and R--2) of G and G- were all above 0.86. The K of all starch gel samples was higher than K- at the same angular frequency, consistent with the changes of G and G--. K and K- decreased with the increase of pre-heating time, indicating that the viscoelastic moduli of starch gels decreased with increasing DSG after full gelatinization. The tanδ of starch gel samples ranged from 0.06 to 0.24 (Supplementary Figure S2). Similarly, a previous study reported starch films exhibiting a tanδ from 0.05 to 0.25 [45]. Moreover, as a dimensionless parameter, tanδ increased with increased pre-heating time, indicating the viscous nature was dominant over the elastic nature. The pre-gelatinization treatment under certain conditions (forming uniform starch pastes with a low DSG) can provide the starch gels relatively high viscoelasticity after full gelatinization. The n and n- values of all starch gels were very similar, indicating that these samples have similar frequency sensitivity.

#### *3.6. Correlation between the DSG and Its Physicochemical Properties*

The physicochemical properties of potato starch as a function of the DSG are shown in Figure 4. Results showed a linear dependent relation between the starch properties and DSG, with their corresponding coefficients of determination (r2) differing. The prominence detection of the two datasets analyzed was less than 0.01, indicating that these starch properties were significantly correlated with the DSG when the significance level was below 0.01. Both the T0 from the DSC test and the temperature at peak tanδ from the temperature sweep of the rheometer were positively correlated with the DSG (Figure 4A,B), indicating that the gelatinization temperature of partially gelatinized potato starch increased in the

reheating process as the DSG increased. The WBC and K values were also positively correlated with the DSG (Figure 4C,G). The ratios of absorbance 1047/1022 cm−<sup>1</sup> were negatively correlated with the DSG, while the ratios 1022/995cm−<sup>1</sup> were positively correlated with the DSG (Figure 4D,E), confirming the loss of the short-range ordered structure of the starch samples with a higher DSG. Moreover, the r2 of 1022/995cm−<sup>1</sup> with DSG was 0.844, which is much higher than that of the 1047/1022cm−<sup>1</sup> with DSG (0.363). Thus, the value of 1022/995 cm−<sup>1</sup> from the FTIR better represents the DSG of partially gelatinized potato starch after hydrothermal treatment. The maximum point of G in the reheating process, K- , and K- of potato starch samples with DSGs higher than 39.41% were also negatively correlated with their DSG, indicating that the viscoelasticity of starch gels decreased with increasing DSG (Figure 4F,H,I).

**Figure 4.** Relationship between the physicochemical properties of potato starch and its degree of gelatinization (**A**: T0 from DSC; **B**: temperature at the peak tanδ from temperature sweep; **C**: WBC at 20 ◦C; **D**: ratios of absorbance 1047/1022 cm−<sup>1</sup> from FTIR; **E**: ratios of absorbance 1022/995 cm−<sup>1</sup> from FTIR; **F**: peak G from temperature sweep; **G**: K value from steady shear test; **H**: K value from frequency sweep; **I**: K-value from frequency sweep).

#### **4. Conclusions**

Native and partially gelatinized potato starch (DSG = 39.41%) cannot form uniform pastes in cold water (10%, *w*/*w*). However, partially gelatinized potato starch with a DSG of 56.11% can form stable paste with a fine shear-thinning property, as well as starch samples with a DSG larger than 56.11%. The apparent viscosity, WBC, and gelatinization onset of partially gelatinized potato starch increased as the DSG increased. Higher starch DSG led to the loss of the short-range ordered structure, and we also found that hydrothermal treatment has a more significant effect on the amount of exposed hydroxyl groups than the ordered and amorphous structures of starch. Partially gelatinized potato starch prepared under certain conditions (form uniform starch pastes in cold water with a low DSG) could form starch gels with relatively high viscoelasticity after reheating. The loss of oval or elliptical structures and the disappearance of birefringence of the starch granules can be clearly observed with increasing DSG. A correlation analysis between the starch physicochemical properties and the DSG further confirmed their linear relationships. The findings are expected help researchers better design the processing conditions for partially gelatinized potato starch and to provide information to better formulate food systems with added potato starch. However, since a heating process is normally required in food processing, further study is still needed to investigate the gelatinization and retrogradation of partially gelatinized potato starch with different DSGs during the reheating process. The molecular mechanism leading to the corresponding gelling behaviors still needs to be revealed.

**Supplementary Materials:** The following are available online at https://www.mdpi.com/article/ 10.3390/foods10051104/s1, Table S1: The gelatinization onset temperatures of native and partially gelatinized potato starch samples pre-heated at 59 ◦C and 60 ◦C for different times (min) by calculating temperatures at the maximum points of Tanδ, Figure S1: Ratios of absorbance 1047/1022 cm−<sup>1</sup> (open symbols) and 1022/995 cm−<sup>1</sup> (solid symbols) of native and partially gelatinized potato starch samples as a function of heating time, Figure S2: Temperature (A, B) and frequency (C, D) dependence of tanδ of native and partially gelatinized potato starch samples (A, C: pre-heated at 59 ◦C; B, D: pre-heated at 60 ◦C).

**Author Contributions:** Conceptualization, F.X. and H.H.; methodology, F.X.; software, F.X.; validation, L.Z., W.L. and Q.L.; formal analysis, F.X.; investigation, W.L.; resources, L.Z.; data curation, F.X.; writing—original draft preparation, F.X.; writing—review and editing, F.W.; visualization, H.Z.; supervision, C.B.; project administration, H.H.; funding acquisition, F.X. and H.H. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Natural Science Foundation of China, grant number: 31601507; the Agricultural Science and Technology Innovation Program, grant number: CAAS-ASTIP-IFST; the China Agricultural Research System, grant number: CARS-09-P27; and the Special Fund for Agro-scientific Research in the Public Interest of China, grant number: 201503001-2.

**Data Availability Statement:** The data presented in this study are available on request from the corresponding author.

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

### **References**

