Establishment of the Flory-Fox Equation and Corroboration of the Fox Equation for Poly(2-vinylpyridine) (P2VP) using Differential Scanning Calorimetry (DSC) Dr. Ronald P. D’Amelia and Evan H. Kreth
Chemistry Department, Hofstra University, Hempstead, NY 11549-0151 Introduction Poly(2-vinylpyridine) (P2VP) is a versatile polymer that holding numerous industrial applications, particularly within the textile and automotive industries. Most notably, P2VP monomer 2-vinylpyrdine is copolymerized with styrene and butadiene, monomers for poly(styrene) and polybutadiene rubber respectively, to form vinylpyridine latex: the copolymer providing the adhesion between the fabric and rubber of vehicle tires. Adhesive applications extend beyond vehicle tires, as P2VP has also found industrial purpose in machinery involving fabric to rubber friction such as belts, hoses, and conveyor systems.
Results
Experimental
Table 1. Glass Transition Temperature (Tg) Data for Various Molecular Weight (Mw) P2VP Mw Mw Onset Tg Half-Cp Tg End Tg Mw Onset Tg Half-Cp Tg
Mw Mn
(°C) 112.79
End Tg (°C) 115.02
110.21
111.86
114.06
112.37
113.87
115.94
944,000
112.41
114.27
116.63
1,220,000
113.31
115.26
117.57
(g/mol) 2,140
(°C) 42.95
(°C) 45.93
(°C) 49.71
Mn
1.03
1.11
(g/mol) 219,000
(°C) 110.86
1.02
3,030
61.22
62.84
65.09
1.09
404,000
1.01
4,050
73.11
76.94
80.11
1.08
650,000
1.05
9,100
96.14
97.96
100.25
1.09
1.00
38,600
105.52
107.99
110.72
1.10
Figure 2. Flory-Fox Plot of Glass Transition Temperature (Tg) vs. Molecular Weight (Mw)
Solvent Blend Technique
Figure 3. Linear Plot of Glass Transition Temperature (Tg) vs. Reciprocal Molecular Weight (Mw -1)
Combinations of different molecular weight P2VP with sufficiently large differences in Tg were first identified. Both samples of P2VP were added to 3 mL glass vials in proportions defined in Table 2 and Table 3, followed by the addition of 200 µL of methanol. A Pasteur pipet was used to aliquot the dissolved P2VP blends directly into a DSC standard aluminum pan atop a hot plate maintained at 160-180°C. The hot plate acted to drive off the methanol which if ignored, would have acted as a plasticizer, producing inaccurate, decreased Tg values. This step was repeated until a desirable amount of P2VP blend (15-20 mg) had accumulated within the DSC standard pan.
Results Figure 6. Glass Transition Temperatures (Tg) for Binary Mixtures of Different Molecular Weight (Mw) P2VP
Figure 1. Polymerization of 2-vinylpyridine monomer to form P2VP Glass transition temperature (Tg), termed the “melting point of amorphous materials” is the temperature at which an amorphous polymer changes from a hard, glassy state to a soft, rubbery one. As the number-average molecular weight (Mn) of the amorphous polymer increases, its Tg also increases but ultimately levels off at a maximum value labeled Tg ∞. The Flory-Fox equation relates these parameters for amorphous polymers and is given below. 𝑇! = 𝑇!,# −
𝐾 𝑀$
The Flory-Fox equation can be rearranged so that the Flory-Fox parameters Tg ∞ and K can be solved graphically. This rearrangement is shown below where the final equation parallels the general equation given for a straight line. Through this manipulation the slope of a plot examining onset Tg versus reciprocal molecular weight Mw -1, represents K for the particular amorphous polymer, while the y-intercept of the same plot denotes Tg ¥. 𝐾 + 𝑇!# 𝑀$ 1 𝑇! = −𝐾 + 𝑇!# 𝑀$ 𝑇! = −
The Tg of a binary mixture of amorphous polymers changes with the weight percent of the components of the binary mixture. This relationship is described by the Fox equation shown below, where w indicates the weight percent of each amorphous polymer. 1 𝑇!,%&'
=
𝑤( 𝑇!,(
+
𝑤) 𝑇!,)
Research Goals 1. To establish the Flory-Fox Equation and associated Flory-Fox parameters Tg ∞ and K for the examined amorphous polymer, poly(2-vinylpyridine) (P2VP). 2. To develop a technique in which homogeneous blends of P2VP could be easily produced. 3. To corroborate the Fox equation for utilizing various binary mixtures (blends) of P2VP of different number-average molecular weights (Mn).
Experimental Poly(2-vinylpyridine) (P2VP) Eleven P2VP samples were obtained from Scientific Polymer Products and used without further purification in order to establish the Flory-Fox and linear plots shown in Figure 2 and Figure 3. The molecular weight (Mw), number average molecular weight (Mn), and polydispersity index (PDI) data for these samples are displayed in Table 1. Combinations of P2VP from Table 1 were utilized to prepare the binary mixtures (blends) of Tables 2 and 3.
Differential Scanning Calorimetry (DSC) Each P2VP sample was packed into a standard aluminum pan and the lid was left laying on top of the sample, unpressed. These samples were analyzed using a Perkin Elmer Pyris 1 DSC with nitrogen serving as the purge gas flowing at 20 mL min -1. Each thermogram was obtained at a rate of 10°C per minute and Tg data was calculated using the “Tg” option found in the Pyris DSC software package. Selected thermograms for various P2VP samples are shown in Figure 4. An indium metal standard was used to calibrate the temperature and enthalpy measurements of the DSC.
Table 2. Glass Transition Temperatures (Tg) for Binary Mixtures of Different Molecular Weight (Mw) P2VP Percent Mw = 4,050
Percent Mw = 38,600
Measured Onset Tg (°C)
Calculated Onset Tg (°C)
102.92
Percent Mw = 3,030
Percent Mw = 219,000
Measured Onset Tg (°C)
Calculated Onset Tg (°C)
0
100
0
100
20.29
79.71
99.47
98.23
19.88
80.12
101.30
99.81
39.68
60.32
95.08
94.14
40.00
60.00
95.74
91.66
60.49
39.51
89.82
90.11
59.82
40.18
86.28
84.84
79.69
20.31
86.19
86.68
79.76
20.24
78.63
100
0
100
0
83.33
Figure 4. DSC Thermograms for the Glass Transitions of Several Selected Molecular Weight (Mw) P2VP
Figure 7. Glass Transition Temperatures (Tg) for Binary Mixtures of Different Molecular Weight (Mw) P2VP
109.41
78.93 73.72
Table 3. Glass Transition Temperatures (Tg) for Binary Mixtures of Different Molecular Weight (Mw) P2VP Percent Mw = 3,030
Percent Mw = 9,100
Measured Onset Tg (°C)
Calculated Onset Tg (°C)
0
100
20.11
79.89
86.57
90.81 86.77
40.32
59.68
84.49
83..05
59.82
40.18
79.73
79.75
79.80
20.20
76.66
100
0
76.64 73.72
Figure 5. Glass Transition Temperatures (Tg) for Binary Mixtures of Different Molecular Weight (Mw) P2VP
Conclusions 1. Flory-Fox equation for P2VP was found to be Tg = 112°C – 1.5e+5°C·g·mol-1Mw -1 (r2 > 0.99). 2. Associated Flory-Fox parameters were evaluated to be Tg ∞ = 112 °C and K = 1.5e+5°C·g·mol-1. 3. A solvent blend technique was successfully developed to create binary mixtures of P2VP, confirmed by the appearance of a single glass transition in all DSC thermograms. 4. The Fox equation Tg -1 = w 1Tg 1-1 + w 2Tg 2-1 was corroborated for various blends of P2VP.
References [1] D’Amelia, R.P.; Kreth, E. H. Establishment of the Flory-Fox Equation for Polymethyl Methacrylate (PMMA) Using Differential Scanning Calorimetry (DSC) and Determination of Relative Tacticity Using Quantitative Nuclear Magnetic Resonance Spectroscopy (qHNMR). Journal of Polymer and Biopolymer Physics Chemistry 2023, 11 (1), 1-10. [2] Fox Jr., T. G.; Flory, P. J. Second-Order Transition Temperatures and Related Properties of Polystyrene. I. Influence of Molecular Weight. Journal of Applied Physics 1950, 21 (6), 581-591. [3] Fox, T. G. and Flory, P. J. The Glass Temperature and Related Properties of Polystyrenes Influence of Molecular Weight. Journal of Polymer Science 1954. 14 (75). 315-319.
Support We acknowledge the support from the Dr. Bruce and Doris Lister Endowed Fellowship in Chemistry Research as well as Hofstra HCLAS Faculty Research & Development Grant. printed by www.postersession.com