Polymerization Kinetics: Screencast
Describes the reaction steps in addition polymerization, using free radical polymerization as an example.
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An introduction to step-growth polymerization.
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Calculates the number-averaged and weight-averaged molecular weights of a polymer, along with its polydispersity.
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Important Equations:
\(P_j\) = concentration of polymer with \(j\) monomer units
\(j\) = number monomer units in the polymer
\(\overline{M_n} = MW_m \dfrac{\sum_j jP_j}{\sum_j P_j} = MW_m \dfrac{\Gamma_1}{\Gamma_0} =\) number average molecular weight
\(\overline{M_w} = MW_m \dfrac{\sum_j j^2P_j}{\sum_j jP_j} = MW_m \dfrac{\Gamma_2}{\Gamma_1} =\) weight average molecular weight
\( \overline{MW_m}\) = molecular weight of monomer
\(\Gamma_0 = \sum_j P_j =\) zero moment of distribution
\(\Gamma_1 = \sum_j jP_j =\) first moment of distribution
\(\Gamma_2 = \sum_j j^2P_j = \) second moment of distribution
\(PD = \dfrac{\overline{M_w}}{\overline{M_n}} = \dfrac{\Gamma_2 \Gamma_0}{\Gamma_1 ^2} =\) polydispersity
\(\overline{DP} = \dfrac{\overline{M_n}}{MW_m} =\) degree of polymerization
\(\overline{DP} =\) average number of repeat units (i.e., average number of monomers in a polymer
Alternate ways to express average molecular weights
\(\overline{M_n} = \sum x_j (jMW_m)\)
\(x_j\) = mole fraction of polymer \(j\)
\(\overline{M_w} = \sum w_j (jMW_m)\)
\(w_j\) = weight fraction of polymer \(j\)
Addition polymerization
\[r_p = k_p \left( \frac{f\,k_d}{k_t} \right) [I_2]^{\frac{1}{2}} [M]\]
where \(r_p\) = rate of polymer formation
\(k_p\) = rate of constant for propagation
\(f\) = initiator efficiency (number less than one)
\(k_d\) = rate constant for dissociation of initiator
\(k_t\) = rate constant for termination
\( [I_2] \) = concentration of initiator
\( [M] \) = concentration of monomer