The Method of Direct and Reverse Phase Portraits as a Tool for Systematizing the Results of Studies of Phase Transitions in Solutions of Thermosensitive Polymers

Abstract

It is shown that a more than significant amount of experimental data obtained in the field of studying systems based on thermosensitive hydrophilic polymers and reflected in the literature over the past decades makes the issue of their systematization and classification relevant. This, in turn, makes relevant the question of choosing the appropriate classification criteria. It is shown that the basic classification feature can be the number of phase transition stages, which can vary from one to four or more depending on the nature of the temperature-sensitive system. In this work, the method of inverse phase portraits is proposed for the first time. It was intended, among other things, to identify the number of phase transition stages. Moreover, the accuracy of this method significantly exceeds the accuracy of the previously used method of direct phase portraits since, for the first time, the operation of numerical differentiation is replaced by the operation of numerical integration. A specific example of the application of the proposed method for the analysis of a previously studied temperature-sensitive system is presented. It is shown that this method also allows for a quantitative comparison between the results obtained by the differential calorimetry method and the turbidimetry method. Issues related to increasing the resolution of the method of direct phase portraits are discussed.

Keywords: classification accuracy; data systematization; inverse phase portrait method; phase transitions; thermograms; thermosensitive polymers; turibidimetry.

Figure 1

Statistics of search results for the keywords “thermosensitive”, “thermoresponsive polymer” in the WoS database by year.

Figure 2

Thermograms of an aqueous solution of C12-PN-AzPy of varying molar masses (concentration: 0.5 mg/mL for polymers of molar masses 5K (1, blue) and 7K (2, orange); 1.0 mg/mL for polymers of molar masses 12K (3, gray) and 20K (4, yellow)) [138].

Figure 3

Turbidity curves of an aqueous solution of C12-PN-AzPy of varying molar masses (concentration: 0.5 mg/mL for polymers of molar masses 5K (1, blue) and 7K (2, orange); 1.0 mg/mL for polymers of molar masses 12K (3, gray) and 20K (4, yellow)) [138].

Figure 4

Comparison of curves $T_t\left(T\right)$ (1, orange) and $s_t\left(T\right)$ (2, blue) obtained from the data of [139]; (a) for curves 1 in Figure 2 and Figure 3, (b) for curves 4 in these figures.

Figure 5

Reverse (a) and direct (b) phase portraits for curves 1 in Figure 2 and Figure 3. 1 and 3—parabolic sections of the phase portrait, 2—intermediate; different colors are used to mark different areas of the same phase portrait.

Figure 6

Reverse (a) and direct (b) phase portraits for curves 2 in Figure 2 and Figure 3; different colors are used to mark different areas of the same phase portrait.

Figure 7

Reverse (a) and forward (b) phase portraits for curves 3 in Figure 2 and Figure 3; different colors are used to mark different areas of the same phase portrait.

Figure 8

Reverse (a) and direct (b) phase portraits for curves 4 in Figure 2 and Figure 3; different colors are used to mark different areas of the same phase portrait.

Figure 9

Dependences of the optical density of solutions of copolymer NIPAAm with 2-HEA with various ratios of hydrophilic chains 50:50 (a), 70:30 (b) on temperature: 0.0125% (1, light blue); 0.025% (2, yellow); 0.05% (3, gray); 0.1% (4, orange); 0.2% (5, dark blue) [139].

Figure 10

Phase portraits: curve 1 in Figure 9a (a), curve 2 in Figure 9a (b), curve 3 in Figure 9a (c), curve 1 in Figure 9b (d), and curve 1 in Figure 9b (e); blue color is a parabolic section, orange is a linear section.

Figure 10

Phase portraits: curve 1 in Figure 9a (a), curve 2 in Figure 9a (b), curve 3 in Figure 9a (c), curve 1 in Figure 9b (d), and curve 1 in Figure 9b (e); blue color is a parabolic section, orange is a linear section.

Figure 10

Phase portraits: curve 1 in Figure 9a (a), curve 2 in Figure 9a (b), curve 3 in Figure 9a (c), curve 1 in Figure 9b (d), and curve 1 in Figure 9b (e); blue color is a parabolic section, orange is a linear section.

Figure 11

An example of processing experimental data, leading to a dependence of the form (5); curve 1—experimental data; curve 2 (orange)—approximation of the section of the experimental curve corresponding to the linear phase portrait using exponential dependence (6); curve 3—the result of dividing the values corresponding to the experimental data by the result of approximation according to Formula (6); curve 4 (black)—approximation of the curve 3 using a formula of the form (2); curve 5 (red)—approximation of the original experimental data using a dependence of the form (8).

Figure 12

Model curve constructed according to Formula (5); $T_{01}=22\mathrm{K}$, ${\tau }_1=10\mathrm{K}$, $T_{02}=30\mathrm{K}$, $\tau =1.2\mathrm{K}$, $D_0=1$.

Figure 13

Phase portrait of the model curve, Figure 12; blue—parabolic section of the phase portrait, gray—linear, orange—intermediate; parabolic and linear approximations are shown by dotted lines in the corresponding colors.