LearnChemE

#### 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 $$j$$

$r_p = k_p \left( \frac{f\,k_d}{k_t} \right) [I_2]^{\frac{1}{2}} [M]$

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