Establishing the Flory-Fox Equation for Polymethyl Methacrylate (PMMA) using Differential Scanning Calorimetry (DSC) and Determining Relative Tacticity using Quantitative Proton Nuclear Magnetic Resonance Spectroscopy (qHMNR) Dr. Ronald P. D’Amelia and Evan H. Kreth
Chemistry Department, Hofstra University, Hempstead, NY 11549-0151 Introduction
Results
Results
Polymethyl methacrylate (PMMA), best recognized by its trade names of Perspex, Lucite, and Plexiglass, is a transparent and rigid thermoplastic. It commonly serves as a substitute for glass due to its lightweight, shatterproof, and scratch-resistant properties.
Table 1: Glass Transition Temperatures (Tg) of Various Peak Molecular Weight (Mp) PMMA
Figure 9: qHNMR Spectrum for 50:50 Isotactic to Syndiotactic Binary Mixture of PMMA
Figure 2: Isotactic PMMA
Figure 3: Syndiotactic PMMA
Figure 1: Structure of PMMA Monomer 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.
Mw Mn
Mp (g/mol)
Onset Tg (°C)
Half-Cp Tg (°C)
End Tg (°C)
Mw Mn
Mp (g/mol)
Onset Tg (°C)
Half-Cp Tg (°C)
End Tg (°C)
1.08 1.11 1.10 1.04 1.04 1.04 1.03 1.02
3,040 4,600 6,940 9,590 13,630 20,520 32,340 46,900
89.034 100.569 110.486 121.961 125.854 129.956 130.973 131.879
91.658 103.342 113.773 125.275 129.289 132.771 134.439 135.039
94.478 106.450 117.060 128.812 132.712 135.802 137.774 138.490
1.02 1.02 1.10 1.04 1.04 1.04 1.03 1.02
72,800 98,550 156,200 210,000 260,900 538,500 766,000 1,020,000
133.571 133.651 134.656 133.450 133.049 134.266 133.171 132.788
136.478 135.721 137.792 137.330 134.878 137.668 134.499 133.723
139.669 138.791 141.160 141.409 138.021 141.099 138.033 137.214
Figure 4: Flory-Fox Plot of Glass Transition Temperature (Tg) vs. Peak Molecular Weight (Mp)
Figure 5: Linear Plot of Glass Transition Temperature (Tg) vs. Reciprocal Peak Molecular Weight (1/Mp)
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.
Proton nuclear magnetic resonance spectroscopy (HNMR) serves as a fundamental tool in determining the structure, and therefore identity, of organic compounds. When applied quantitatively (qHNMR), it can also be used to determine relative concentrations of compounds in solution, and the stereochemistry associated with polymers, or tacticity.
Research Goals 1. To establish the Flory-Fox Equation, and associated values of Tg∞ and K, for the examined polymer, polymethyl methacrylate (PMMA). 2. To verify the Fox equation with various binary mixtures of PMMA of different numberaverage molecular weights. 3. To evaluate the effectiveness of quantitative proton Nuclear Magnetic Resonance spectroscopy (qHNMR) as a method for determining relative tacticity in PMMA.
Experimental Polymethyl Methacrylate (PMMA) Seventeen, predominantly syndiotactic PMMA samples of various molecular weights were used to establish the Flory-Fox equation and its linear plot (Figures 4 and 5). These samples were sourced from Agilent Technologies and all boasted low polydispersity indices (Table 1). The PMMA samples utilized in the binary mixtures (Table 2 and Figure 7) were sourced from Scientific Polymer Products and did not contain any high degree of tacticity.
Table 4: Corresponding Chemical Shifts in qHNMR of Isotactic and Syndiotactic PMMA Table 2: Glass Transition Temperatures (Tg) for Binary Mixtures of Different Molecular Weight (Mw) PMMA Proportion of Mw = 15,000
Proportion of Mw = 35,000
Measured Onset Tg (°C)
Theoretical Onset Tg (°C)
Proportion of Mw = 15,000
Proportion of Mw = 75,000
Measured Onset Tg (°C)
Theoretical Onset Tg (°C)
1.00 0.80
0.00 0.20
82.625 87.866
82.625 86.001
1.00 0.80
0.00 0.20
83.063 86.662
83.063 85.039
0.60 0.40
0.40 0.60
93.368 94.248
89.549 93.528
0.60 0.40
0.40 0.60
88.639 89.708
87.034 89.179
0.20 0.00
0.80 1.00
98.647 102.675
97.955 102.675
0.20 0.00
0.80 1.00
93.085 93.686
91.321 93.686
Figure 6: DSC Thermograms of the Glass Transitions For Several Peak Molecular Weight (Mp) of PMMA
Figure 7: Glass Transition Temperatures (Tg) for Binary Mixtures of Different Molecular Weight (Mw) PMMA
Differential Scanning Calorimetry (DSC)
In order to achieve uniform binary mixtures or blends, used in Table 2 and Figure 7, a hot melt blend technique was adopted. This technique involved utilizing a hot plate to heat both PMMA samples until they were fluid, and mechanically mixing them until a homogeneous blend was obtained. The PMMA blend was then cooled rapidly and placed into a standard aluminum pan for thermal analysis, where a single Tg was observed, confirming the validity of the technique.
Nuclear Magnetic Resonance Spectroscopy (NMR) The proton NMR spectra were obtained using a 400 MHz JEOL model ECS-400 NMR spectrometer. The PMMA samples were dissolved in deuterated chloroform (CDCl 3) at concentrations ranging from 25-30 mg/mL. The JEOL Delta NMR software version 6.0.0 (Windows) was used to analyze the individual spectra. A typical NMR spectrum for a 50:50 binary mixture of isotactic to syndiotactic PMMA is shown in Figure 9. The corresponding chemical shifts for the hydrogens in isotactic and syndiotactic PMMA are shown in Table 4.
Methyl
1.263
More Shielded Methylene
1.558 1.595
Less Shielded Methylene
2.177 2.213
Ester
3.656
Syndiotactic Hydrogens Chemical Shift (ppm) Methyl
0.913 1.078
Methylene
1.873
Ester
3.656
Conclusions
Each PMMA 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. Each thermogram was obtained at a rate of 10°C per minute and each glass transition temperature was calculated using the “Tg” option found in the Pyris DSC software package. Selected thermograms for various PMMA samples are shown in Figure 6. An indium metal standard was used to calibrate the temperature and enthalpy measurements of the DSC.
Hot Melt Blend Technique
Isotactic Hydrogens Chemical Shift (ppm)
Figure 8: Percent Isotactic PMMA in Binary Mixtures by Gravimetric Analysis and qHNMR of Various Hydrogens
1. The Flory-Fox equation for PMMA was evaluated to be: Tg = 135°C – 1.4 x 105 °Cᐧgᐧmol-1/Mn. 2. Tg∞ and K were evaluated to be 135°C and 1.4 x 105 °Cᐧgᐧmol-1 respectively for predominantly syndiotactic PMMA. 3. The Fox equation, 1/Tg = w1/Tg1 + w2/Tg2, was verified for various binary mixtures of PMMA. 4. HNMR can be used to differentiate between primarily isotactic or syndiotactic PMMA samples. 5. Peak integrations of the methylene or methyl hydrogens in qHNMR spectra of PMMA can be used to determine relative isotacticity or syndiotacticity in PMMA samples.
References [1] D’Amelia, R.P.; Khanyan, B. An Experimental Review: Evaluation of the Flory-Fox Equation for the Relationship of Glass Transition Temperature (Tg) vs Molar Mass of Polystyrene Using Differential Scanning Calorimetry (DSC). JPBPC 2022, 10 (1), 10-17. [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] Ober, C.K. Polymer tacticity in simulated NMR spectra. Journal of Chem. Ed. 1989, 66 (8), 645.
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