# ch02 - CHAPTER 2 SOLUTIONS 2.1 Using the GAMS program in...

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2-1 CHAPTER 2 SOLUTIONS 2.1 Using the GAMS program in Example 2.2, a method could not be found to locate the repeat units having the second and third lowest values of the objective function, Z. Initially, an attempt was made to place a lower bound on Z, adjusting it upward from Z = 0.0007 (the minimum value) until the solution with the next lowest Z is located. In the solution obtained by GAMS, small fractional numbers of groups were obtained. N e x t , n 7 was set equal to zero and the following inequalities were added: 393 373 g T 75 . 1 25 . 1 ρ which produced the solution: ---- 63 VARIABLE TG.L = 379.3233 VARIABLE RHO.L = 1.2804 VARIABLE W.L = 0.0244 VARIABLE n1.L = 7.0000 VARIABLE n2.L = 2.0000 VARIABLE n3.L = 0.0000 VARIABLE n4.L = 7.0000 VARIABLE n5.L = 0.0000 VARIABLE n6.L = 0.0000 VARIABLE n7.L = 0.0000 VARIABLE Z.L = 15.0395 For this repeat unit, -(CH 2 ) 7 (CO) 2 (O) 7 -, the glass transition temperature is close to 383 K, but significant differences are associated with the specified density (1.5 g/cm 3 ) and water adsorption (0.005 g H 2 O/g polymer). Using the inequalities: 393 373 g T 0 . 2 0 . 1 another solution is obtained: 63 VARIABLE TG.L = 385.7143 VARIABLE RHO.L = 1.0323 VARIABLE W.L = 0.0177 VARIABLE n1.L = 6.0000

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2-2 VARIABLE n2.L = 1.0000 VARIABLE n3.L = 0.0000 VARIABLE n4.L = 0.0000 VARIABLE n5.L = 0.0000 VARIABLE n6.L = 0.0000 VARIABLE n7.L = 0.0000 VARIABLE Z.L = 6.5595 For this repeat unit, -(CH 2 ) 6 CO-, the glass transition temperature is close to 383 K, the difference associated with the specified density (1.5 g/cm 3 ) is increased, and that associated with the water adsorption (0.005 g H 2 O/g polymer) is decreased. Note that better solutions could not be found. When the seventh group is included, only the solution in Example 2.2 is obtained. These results can be reproduced by modifying the GAMS program listed in the file, EXER2-2.doc, on the CD-ROM.
2-3 2.2 This solution is obtained by eliminating the seventh group, -CHCl-, from the GAMS program in Example 2.2. The resulting GAMS program and solution are: VARIABLES n1, n2, n3, n4, n5, n6, TG, RHO, W, H, V, Y, M, STG, SRHO, SW, Z; POSITIVE VARIABLES STG, SRHO, SW, W, H, V, Y, TG, M, RHO; INTEGER VARIABLES n1, n2, n3, n4, n5, n6; n1.LO = 0; n1.UP = 7; n2.LO = 0; n2.UP = 7; n3.LO = 0; n3.UP = 7; n4.LO = 0; n4.UP = 7; n5.LO = 0; n5.UP = 7; n6.LO = 0; n6.UP = 7; M.LO = 14; V.LO = 10; H.LO = 3.3E-5; Y.LO = 2700; W.LO = 0; W.UP = 0.18; TG.LO

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## This homework help was uploaded on 04/10/2008 for the course CHE 233W taught by Professor Debelak during the Spring '08 term at Vanderbilt.

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ch02 - CHAPTER 2 SOLUTIONS 2.1 Using the GAMS program in...

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