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CHM 585 / 490

Chapter 7Properties

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Chapter 7

• Molecular weight• Tg• Melting Point

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Chain Entanglement

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The degree of polymerization (DP)

• DP in a polymer molecule is the number, n, of repeating units in the polymer chain.

  • The molecular weight of a particular polymer

molecule is a product of the degree of polymerization and the molecular weight of the repeating unit. For instance a particular polyethylene molecule with DP = 1000 will have a molecular weight of 28,000.

C CH

H

H

H( )

n

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Averaging

• Because polymeric materials do not consist of strictly identical molecules, but instead are a mixture of many species having different values of DP, the DP of the material only is an average value, . Hence, measured polymer molecular weights are only average values.

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Weight Average / Number Average

• The number average is the simple arithmetic mean, representing the total weight of the molecules present divided by the total number of molecules

• The probability factor in a weight-average emphasizes the mass of the molecules so that the heavier molecules are more important.

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The ratio of the weight-average and number-average molecular weights,

    , is a measure of the polydispersity of a polymer mixture - how widely distributed the range of molecular weights are in the mixture. A ratio that is around 1.0 indicates that the range of molecular weights in the mixture is narrow; a high ratio indicates that the range is wide.

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Start Destination Miles1: Atlanta, GA 2: Columbia, SC 2102: Columbia, SC 3. Charlotte, NC 903: Charlotte, NC 4. New York, NY 6204. New York, NY 5. Los Angeles, CA 2790

Suppose that you want to travel from Atlanta to Los Angeles, visiting your friends along the way. Unfortunately your friends live only on the eastern and western coasts, leading to a somewhat unconventional journey.

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Start Destination Miles1: Atlanta, GA 2: Columbia, SC 2102: Columbia, SC 3. Charlotte, NC 903: Charlotte, NC 4. New York, NY 6204. New York, NY 5. Los Angeles, CA 2790

The number-average of the miles traveled in the four legs of the journey is 928 miles. This is the average distance traveled in each leg of the journey. It places equal emphasis on each leg.The mass-average of the miles traveled in the four legs of the journey is 2216 miles. This average places a greater emphasis on the leg of the journey with the largest "mass" - that is the fourth leg in which you travel 2790 miles. It is more representative of the major part of your journey.

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If you look at the numbers you can see that the average person doesn't live in a town of a population of 180,000. Take a look there. most of the people in the combined populations of the four towns live in Memphis, a town with a lot more than 180,000 people. So how do we calculate the size of town that the average person lives in, if the simple average doesn't work?

What we need is a weighted average.

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Take Memphis. It has a population of 700,000. The total population of our four cities is 723,500. So the fraction of people who live in Memphis is...

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2 ChainsOne at 10,000;One at 100,000

• Mn = (100,000 + 10,000) /2 = 55,000• Mw

– 100,000 / 110,000 = .91– 10,000 / 110,000 = .09– (100,000 x .91) + (10,000 x .09) = 91,900– Mw = 91,900

• Polydispersity = Mw/Mn = 91,900/55,000 = 1.7

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Glass Transition Tg

The polymer samples may be thought of as a crowd of people on a dance floor. While each whole body tends to stay in the same spot, various arms, legs, and whatnot are changing position a lot. When the temperature drops below the Tg, for polymers the party's over, and the long-range segmental motion grinds to a halt. When this long-range motion ceases, the glass transition occurs, and the polymer changes from being soft and pliable to being hard and brittle.

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How easily the chains move.

A polymer chain that can move around fairly easily will have a very low Tg, while one that doesn't move so well will have a high one. This makes sense. The more easily a polymer can move, the less heat it takes for the chains to commence wiggling and break out of the rigid glassy state and into the soft rubbery state.

22For polysulfone Tg > 500C; flexible ether linkages increase mobility and bring the Tg to 190C

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Plasticizers

• Sometimes, a polymer has a Tg that is higher than we'd like. That's ok, we just put something in it called a plasticizer. This is a small molecule which will get in between the polymer chains, and space them out from each other. We call this increasing the free volume. When this happens they can slide past each other more easily.

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DOP

OO

OO

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Tg versus Melting Point.• Melting is a transition which occurs in crystalline

polymers. Melting happens when the polymer chains fall out of their crystal structures, and become a disordered liquid.

• The glass transition is a transition which happens to amorphous polymers; that is, polymers whose chains are not arranged in ordered crystals, but are just strewn around in any old fashion, even though they are in the solid state.

• But even crystalline polymers will have a some amorphous portion. This portion usually makes up 40-70% of the polymer sample. This is why the same polymer can have both a glass transition temperature and a melting temperature.