### SimuLab 4: The Homopolymer Collapse

 You will be able to: a) Understand the thermodynamics of the homopolymer collapse transition; b) Determine the critical q-point.; c) Compare the process with the condensation of liquid near the critical density.

1. Open Universal Application. Press on Play Movie and select Collapse.mov. Press Forward.

~ You see a protein of 256 monomers in the fully unfolded state at high temperature. We will slowly cool down the system taking away the energy. Watch the movie from the beginning to the end. The protein gradually changes its shape from the unfolded irregular coil to a collapsed globule of roughly spherical shape.
~ Copy the table below:

 time temperature Radius of Gyration Potential Energy 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000 13000 14000 15000 16000 17000 18000 19000 20000 21000

2. Rewind the movie till beginning. Reset the Averaging for Movies window and record the values of temperature, Radius of Gyration and potential energy into the table each 1000 units time till time 21000. Press Forward.

 Q2.29: Construct the Temperature, Radius of Gyration and Potential Energy vs. time graphs. Does the temperature vs. time graph have a plateau like in freezing?

#### Simulab 4

A2.29: The temperature vs. time graph does not have a plateau like in freezing instead it have an inflexion point at the critical point named the q-point. The graphs of potential energy and radius of gyration has the maximal local slope in the vicinity of this point. The slope of this graph is the heat capacity CV that has is maximum near the q-point. For very long polymer chain the heat capacity will have infinitely sharp and high peak at the q-point.

 time temperature Radius of Gyration Potential Energy 1000 2.402 88.9 -137.61 2000 2.215 78.98 -148.76 3000 2.005 124.49 -152.42 4000 1.882 66.28 -180.6 5000 1.801 66.77 -218.98 6000 1.771 50.23 -252,61 7000 1.627 48.29 -282.43 8000 1.610 41.50 -337.19 9000 1.561 39.20 -366.98 10000 1.496 35.92 -409.60 11000 1.429 34.96 -442.11 12000 1.372 34.78 - 476.09 13000 1.323 32.83 -510.07 14000 1.269 32.11 -537.24 15000 1.225 31.21 -564.97 16000 1.183 32.08 -593.56 17000 1.135 31.01 -620.74 18000 1.090 30.26 -648.88 19000 1.060 29.11 -678.07 20000 1.013 29.35 -695.46 21000 0.979 28.93 723.70