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LOOK AT THE UPLOADED PICTURE AND SOLVE ALL QUESTIONS ( a to d ) UNDERSTANDBLY PLEASE THANK YOU: One of the distinguishing features of a
LOOK AT THE UPLOADED PICTURE AND SOLVE ALL QUESTIONS a to d UNDERSTANDBLY PLEASE THANK YOU: One of the distinguishing features of a lightly crosslinked polymer
material is its ability to imbibe and retain a large volume of solvent. Examples include hot melt
adhesives, soft contact lenses, diapers, and biological tissues. Clearly, swollen networks are of
fundamental importance in many areas of materials and biological sciences. In this question, I
ask you to work on two aspects of swelling phenomenon: equilibrium swelling, ie how much
solvent a network can take up and the elastic modulus of a swollen network.
Consider polyisoprene chains with with the extent of vulcanization
which resulted in average of crosslinks per chain and The density of
polyisoprene is ole.
a pts Suppose this polymer network is exposed to a reservoir of cyclohexane at
room temperature. According to FloryRehner theory, equilibrium swelling is reached
when
Estimate and find the resulting volumetric
expansion at swelling equilibrium defined in part
b pts You will now estimate the shear modulus of the swollen network. Suppose a
network formed at dry volume and then swollen with a solvent to a new volume
The volume fraction of the polymer in the resulting gel is Assuming the
swelling is isotropic, the components of the end to end vector of each strand is
swollen by Therefore, the extension ratios in the definition of
entropy of a polymer network, that is are multiplied
by a factor Starting from the resuOne of the distinguishing features of a lightly crosslinked polymer material is its ability to imbibe and retain a large volume of solvent. Examples include hot melt adhesives, soft contact lenses, diapers, and biological tissues. Clearly, swollen networks are of fundamental importance in many areas of materials and biological sciences. In this question, I ask you to work on two aspects of swelling phenomenon: equilibrium swelling, ie how much solvent a network can take up and the elastic modulus of a swollen network.
Consider polyisoprene chains with M gmol with the extent of vulcanization
which resulted in average of crosslinks per chain and Mx The density of
polyisoprene is gmole
a pts Suppose this polymer network is exposed to a reservoir of cyclohexane at
room temperature. According to FloryRehner theory, equilibrium swelling is reached when
i
v
ln
e
e
ee v
e
e
NV
Avg
o
e
: equilibrium volume fraction of polymer in swollen gel
: polymersolvent interaction parameter
v : number of elastically effective strands e
where
v : molar volume of the solvent
V
: volume of the dry polymer n
o
etwork
The molar volume of cyclohexane is cm Estimate and find the resulting volumetric
e
expansion at swelling equilibrium defined in part b
b pts You will now estimate the shear modulus of the swollen network. Suppose a
network formed at dry volume Vo and then swollen with a solvent to a new volume V The volume fraction of the polymer in the resulting gel is Vo V Assuming the
swelling is isotropic, the x y z components of the end to end vector of each strand is
kv
are multiplied
S
e
z
x
y
Starting from the resulting entropy change of the swollen network
GG
dry
swelling equilibrium in cyclohexane, ie e and in dry form.
swollen by V Vo Therefore, the extension ratios in the definition of entropy of a polymer network, that is by a factor upon deformation and find the nominal stressextension ratio relationship for a swollen network.
c pts What is the ratio of the moduli in swollen and dry state
d pts Find the shear modulus of the polyisoprene network described above at
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