A04_ENGR 1600 polym MWD activity

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Last Name First Name Section Number Instructor Name Wang Nancy 6 j. shi ENGR1600: Materials Science for Engineers Interactive Activity 04 Polymer Molecular Weight Distributions Introduction. Plastic materials are made of polymer molecules. Polymers are long chain molecules composed of repeating chemical units. But how long is a “long” chain? A chain of just a few repeat units would be a liquid, ten or so an oil, and 30 or so a soft waxy material. Engineering plastics are composed of much longer chains than that – many hundreds or thousands of repeating units per chain. Averages . How long is a polymer chain? That’s like asking “How tall is a human being?”. You might guess 5 feet and 6 inches on average . But many people are shorter and many are taller than that. Same thing goes for polymers: any given sample of engineering plastic is composed of polymer chains with a broad distribution of chain lengths. Some chains are much longer than average, some are much shorter. We can find the number-average chain length ( DP n ) as the simple arithmetic mean. It’s just the total sum of all chain lengths divided by the total number of chains in the sample: ∑(𝐷𝑃 𝑖 × ? 𝑖 ) total length of all chains combined 𝐷𝑃 ? = ∑? 𝑖 = total number of chains [no units] where DP is the “degree of polymerization” which is just a fancy way to say “chain length”, and n is the number of chains in the population having a particular DP. The subscripts i refer to the i th slice in the distribution (like one bar in a histogram). For example, if there are 5 chains of length 90 and 6 chains of length 110, then DP n = (5*90 + 6*110) / (5+6) ≅ 101. It follows that the molecular weight [units of grams/mole ] of the polymer molecules is also a broad distribution. It is easy to interconvert between chain length and MW if we know the molar mass of the repeating unit ( m ). For example, if I have 100 repeating units of a monomer that has a molar mass of m = 28 g/mol, then the whole chain has a MW of 2800 g/mol. 𝑀 𝑖 = 𝐷𝑃 𝑖 × ? Since m is a constant, it also follows that the number-average molecular weight M n is: ∑(𝑀 𝑖 × ? 𝑖 ) total mass of all chains 𝑀 ? = ∑? 𝑖 = total number of chains [g/mol] Knowing the M n is useful, but it’s not enough information. We also need to know about the broadness of the distribution because it impacts the properties of the material – even if the simple number-average is the same. Why? Think about two populations of people that both have an average height of 5 feet and 6

inches. One has a very narrow distribution with all people somewhere between 5 and 6 feet tall. The other has a very broad range of heights, with some people as short as 3 feet and some others as tall as 8 feet! Which population would have the better basketball team? If we want to know about the broadness, a second useful average is the weight-average molecular weight M w . It is the average taken in terms of weight of chains w i rather than number of chains n i . This kind of average (which in statistics is c alled the “second moment of the distribution”) puts more emphasis on the longer chains and less on the shorter ones (like you would do when picking the tallest people in the population for the basketball team). Thus, M w is always greater than M n . The only exception is when all chains in the population have exactly the same length, in which case M n = M w (that’s never the case for plastics, but it is the case for biopolymers like proteins and DNA). We can write this weighted average mathematically as follows. It has the same form as the equation for M n given above. ∑(𝑀 𝑖 × 𝑤 𝑖 ) 𝑀 𝑤 = ∑𝑤 𝑖 [g/mol] Where w i is the weight of the chains in the i th slice of the population. The weight of the chains of a given mass is equal to the number of such chains times the mass of each. For example, if I have 10 chains of 2,800 g each, together they weigh in at 28,000 g in total: 𝑤 𝑖 = 𝑀 𝑖 × ? 𝑖 We can plug that into the expression for M w above and get an equivalent way to write it as it appears in your textbook: 𝑀 𝑤 [g/mol] For any given distribution, we can calculate the number-average M n and the weight-average M w . Our measure of the broadness of the distribution is the ratio M w / M n , which we call the “dispersity” and denote with the symbol Ð (pronounced “ D-stroke ”). Your textbook uses the outdated nomenclature of “polydispersity index” (PDI), which means the same thing as Ð. The higher the Ð, the broader the distribution and vice versa. 𝑀 𝑤 Ð= ≥1 𝑀 ? When polymers are synthesized in chemistry laboratories, conventional techniques are expected to give a product with Ð = 2, which is the most likely outcome for a random statistical polymerization process. Modern day cutting-edge chemistry methods (using fancy catalysts or other magic fairy dust) can give very narrow distributions with dispersity as low as Ð < 1.05. In this activity, you will calculate M n , M w , and Ð for two samples of polystyrene (PS). PS is a common polymer used in plastics, which has the chemical structure shown below. The molar mass of the styrene

repeat unit is 104 g/mol. Sample A was made by a conventional method (which gives a broad distribution) and Sample B was made by more advanced techniques (which gave very narrow distribution). These two samples have identical chemical composition, and as you will see, they have the same M n . The only difference is the broadness of the distribution. We will then explore how this difference plays a role in determining the mechanical properties of the material, even though the number average is the same. This demonstrates why we should care about M w and Ð. Activity Instructions. 1. Download the Excel sheet for Activity #4 from LMS and open the file. You will find two molecular weight distributions for samples A and B. The number of chains n i having a given chain length DP i are listed for each sample. 2. Fill in the table by computing M i , w i , etc. and then compute the relevant summations. As the data for Mi are populated, notice that the graph should display the two distributions. 3. Using the equations given above, compute the M n , M w , and Ð for both samples and enter them in the table below. Express values to 3 significant figures. 4. Upload your Excel Document along with the answer to the Discussion questions below Sample M n (g/mol) M w (g/mol) Ð A 168654 375215 2.22 B 168553 170684 1.01 The mechanical properties of polystyrene have been investigated as a function of molecular weight. Generally speaking, polymers become stronger and stretchable as the M W increases. The graphs below provide data on two samples of PS: one with a very narrow distribution (Ð ~ 1.01) and the other with a broad distribution (Ð ~ 2.2). For both samples, the tensile strength (how much force can it hold before breaking) and the elongation (how much you can stretch it before it breaks) is plotted as a function of M n , the number average molecular weight.

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Discussion Questions . 1. For each sample A and B, calculate the percentage of chains that have a MW greater than 200,000 g/mol (200 kg/mol). A=23.4% B=3.125% 2. Which sample (A or B) will have the higher elongation at break? Sample a has higher elongation at break. 3. Which sample (A or B) will have the higher tensile strength? Sample a has higher tensile strength since it has the higher elongation at break point. 4. Why do you think the PS with a broad distribution of chain lengths has different mechanical properties as compared to the PS with a narrow distribution – even when the M n values are nearly identical? The differing chain lengths allows PS to undergo more mechanical changes rather than the uniform chain lengths of the narrow distribution of PS