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MANE/ENGR 2220 Structure & Properties of Materials 1. The following table lists molecular weight data for some polymer. Compute (a) the number-average molecular weight, (b) the weight-average molecular weight. (c) If it is known that this material's degree of polymerization is 1165, which one of the polymers listed in Table 14.3 is this polymer? Why? Molecular Weight Range g/mol 15,000–30,000 30,000–45,000 45,000–60,000 60,000–75,000 75,000–90,000 90,000–105,000 105,000–120,000 120,000–135,000
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  MANE/ENGR 2220 Structure & Properties of Materials 1. The following table lists molecular weight data for some polymer. Compute (a) the number-average molecular weight, (b) the weight-average molecular weight. (c) If it is nown that this material!s degree of polymeri ation is 11#$, which one of the polymers listed in Table 1%.& is this polymer' hy'  Molecular Weight  Range g/mol    i w i 1$,***+&*,****.*$*.*&*,***+%$,****.**.*%%$,***+#*,****.1#*.11#*,***+$,****.%*.*$,***+*,****.#*. *,***+1*$,****.1*.1# 1*$,***+1*,****.*/*.11*,***+1&$,****.**.*$ Solution(a) From the tabulated data, we are asked to compute  0 n , the number-average molecular weight !his is carriedout belowMolecular wt angeMean  0  i   i   i  0  i #$,%%%-%,%%%'',$%%%%$##'$%,%%%-$,%%%,$%%%%'*'$$,%%%-*%,%%%$',$%%%#*+%%*%,%%%-$,%%%*,$%%%'#*,'%%$,%%%-%,%%%+',$%%%'*'#,$%%,%%%-#%$,%%%,$%%%#'##,%%#%$,%%%-#'%,%%%##',$%%%%+%%%#'%,%%%-#$,%%%#',$%%%%'''$%   g.mol$%,'// ∑  iin  0   ) 0   (b) From the tabulated data, we are asked to compute  0 w , the weight-average molecular weight !hisdetermination is performed as follows0Molecular wt # of   MANE/ENGR 2220 Structure & Properties of Materials angeMean  0  i w i w i  0  i #$,%%%-%,%%%'',$%%%%'$%%,%%%-$,%%%,$%%%%#$%%$,%%%-*%,%%%$',$%%%##$$*%,%%%-$,%%%*,$%%%'%#,$%%$,%%%-%,%%%+',$%%%''','$%,%%%-#%$,%%%,$%%%#*#$,*%%#%$,%%%-#'%,%%%##',$%%%#'#,$%%#'%,%%%-#$,%%%#',$%%%%$*$   g.mol+,$// ∑  iiw  0  w 0   (c) 1e are now asked if the degree of pol2meri3ation is ##*$, which of the pol2mers in !able # is this material45t is necessar2 to compute m  in 67uation #* as  g.mol$'*/ ##*$g.mol',$%//  12  0  m  n !he repeat unit molecular weights of the pol2mers listed in !able # are as follows0Pol2eth2lene--'+%$ g.molPol2(vin2l chloride)--*' g.molPol2tetrafluoroeth2lene--#%%%' g.molPol2prop2lene--'%+ g.molPol2st2rene--#%# g.molPol2(meth2l methacr2late)--#%%## g.molPhenol-formaldeh2de--##* g.mol 82lon *,*--''*' g.molP6!--#'#* g.molPol2carbonate--'$' g.mol!herefore, Pol2(vin2l chloride) is the material since its repeat unit molecular weight is closest to that calculated above . The density and associated percent crystallinity for two polymer materials are as follows3  ρ  (  g/cm 3 ) crystallinity ( % ) 1.1&$1.& ' of   MANE/ENGR 2220 Structure & Properties of Materials 1.1$#%. (a) Compute the densities of totally crystalline and totally amorphous polymer.(b) etermine the density of a specimen having $&./4 crystallinity. Solution(a) 1e are asked to compute the densities of totall2 cr2stalline and totall2 amorphous pol2mer ( ρ c  and ρ a  from67uation #+) From 67uation #+ let C  / % cr2stallinit2#%% , such that   C   / ρ c ( ρ  s   −   ρ a ) ρ  s ( ρ c   −   ρ a ) earrangement of this e9pression leads to   ρ c ( C  ρ  s −ρ  s )  : ρ c ρ a   −   C  ρ  s ρ a  / % in which ρ c  and ρ a  are the variables for which solutions are to be found Since two values of ρ  s  and C   are specified in the problem, two e7uations ma2 be constructed as follows0   ρ c ( C  1 ρ  s 1   −   ρ  s 1 )   +   ρ c ρ a   −   C  1 ρ  s 1 ρ a   =  0   ρ c ( C  ' ρ  s '   −   ρ  s ' )   +   ρ c ρ a   −   C  ' ρ  s ' ρ a   =   % 5n which ρ  s #  / ##' g.cm  , ρ  s '  / #'#$ g.cm  ,  C  # / %$#, and C  '  / %*' Solving the above two e7uations for ρ a  and ρ c  leads to   ρ a   =   ρ  s # ρ  s ' ( C  #   −   C  ' ) C  # ρ  s #   −   C  ' ρ  s ' &&&&& g.cm%+/g.cm'#$#)*'%(g.cm#&'#)$#&%( )*'%$#&%(g.cm'#$#g.cm#&'#  / )()( ))(( −− ;nd  of   MANE/ENGR 2220 Structure & Properties of Materials   ρ c  /   ρ  s # ρ  s ' ( C  '   −   C  # ) ρ  s ' ( C  '   −   # )   −   ρ  s # ( C  #   − # ) &&&&& g.cm#$'$/)#$#&%(g.cm#&'#)#*'%(g.cm'#$# )$#&%*'%(g.cm'#$#g.cm#&'#  / )()( ))(( −−−− (b) 8ow we are asked to determine the densit2 of a specimen having $+< cr2stallinit2 Solving for ρ  s  from67uation #+ and substitution for ρ a  and ρ c  which were computed in part (a) 2ields   ρ  s  / −ρ c ρ a C  ( ρ c −ρ a ) −ρ c &&&&& g.cm$'$#g.cm+%g.cm$'$#)$&+%( g.cm+%g.cm$'$#  / )())(( −−− / ## g.cm  &. The tensile strength and number-average molecular weight for two poly(methyl methacrylate)materials are as follows3 Tensile Strength (  MPa )  Number-Average Molecular Weight (  g/mol  ) 1*&*,***1*#*,***  5stimate the number-average molecular weight that is re6uired to give a tensile strength of 1/$ 02a. Solution!his problem gives us the tensile strengths and associated number-average molecular weights for two pol2(meth2lmethacr2late) materials 67uation #$ cites the dependence of the tensile strength on  0 n  !hus, using the data provided in the problem statement, we ma2 set up two simultaneous e7uations from which it is possible to solve for the twoconstants T7  =  and  8  !hese e7uations are as follows0 mol  g  8T7  .%%%,&% /MPa#%  − ∞   170 MPa= T7  ∞ −  8 60,000 g/mol  of 
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