We apply the time evolution of grain size distributions by accretion and coagulation found in our previous work to the modelling of the wavelength dependence of interstellar linear polarization .
We especially focus on the parameters of the Serkowski curve K and \lambda _ { \max } characterizing the width and the maximum wavelength of this curve , respectively .
We use aligned silicate and non-aligned carbonaceous spheroidal particles with different aspect ratios a / b .
The imperfect alignment of grains with sizes larger than a cut-off size r _ { V, cut } is considered .
We find that the evolutionary effects on the polarization curve are negligible in the original model with commonly used material parameters ( hydrogen number density n _ { \mathrm { H } } = 10 ^ { 3 } cm ^ { -3 } , gas temperature T _ { \mathrm { gas } } = 10 Â K , and the sticking probability for accretion S _ { \mathrm { acc } } = 0.3 ) .
Therefore , we apply the tuned model where the coagulation threshold of silicate is removed .
In this model , \lambda _ { \max } displaces to the longer wavelengths and the polarization curve becomes wider ( K reduces ) on time-scales \sim ( 30 - 50 ) ( n _ { \mathrm { H } } / 10 ^ { 3 } \mathrm { cm } ^ { -3 } ) ^ { -1 } Myr .
The tuned models at { { { { T \mathrel { \mathchoice { \vbox { \offinterlineskip \halign { \cr } $ \displaystyle < $ \cr$% \displaystyle \sim$ } } } { \vbox { \offinterlineskip \halign { \cr } $ \textstyle < $ \cr$% \textstyle \sim$ } } } { \vbox { \offinterlineskip \halign { \cr } $ \scriptstyle < $ \cr$% \scriptstyle \sim$ } } } { \vbox { \offinterlineskip \halign { \cr } $ \scriptscriptstyle < $% \cr$ \scriptscriptstyle \sim$ } } } } 30 ( n _ { \mathrm { H } } / 10 ^ { 3 } \mathrm { cm } ^ { -3 } ) ^ { -1 } Â Myr and different values of the parameters r _ { V, cut } can also explain the observed trend between K and \lambda _ { \max } .
It is significant that the evolutionary effect appears in the perpendicular direction to the effect of r _ { V, cut } on the K – \lambda _ { \max } diagram .
Very narrow polarization curves can be reproduced if we change the type of particles ( prolate/oblate ) and/or vary a / b .