  We present results of the coefficient of thermal expansion for the frustrated
quasi-two-dimensional molecular conductor $\theta$-(BEDT-TTF)$_2$RbZn(SCN)$_4$
for temperatures 1.5 K $\leq T \leq$ 290 K. A pronounced first-order phase
transition anomaly is observed at the combined charge-order/structural
transition at 215 K. Furthermore, clear evidence is found for two separate
glasslike transitions at $T_{\mathrm{g}}$ = 90-100 K and
$T_{\mathrm{g}}^\dagger$ = 120-130 K, similar to previous findings for
$\theta$-(BEDT-TTF)$_2$CsZn(SCN)$_4$ and $\theta$-(BEDT-TTF)$_2$CsCo(SCN)$_4$,
reported in T. Thomas et al., Phys. Rev. B 105, L041114 (2022), both of which
lack the charge-order/structural transition. Our findings indicate that these
glasslike transitions are common features for the
$\theta$-(BEDT-TTF)$_2MM^\prime$(SCN)$_4$ family with $M$ = (Rb, Cs) and
$M^\prime$ = (Co, Zn), irrespective of the presence or absence of charge order.
These results are consistent with our model calculations on the glasslike
dynamics associated with the flexible ethylene endgroups of the BEDT-TTF
molecules for various $\theta$-(BEDT-TTF)$_2MM^\prime$(SCN)$_4$ salts,
predicting two different conformational glass transitions. Moreover,
calculations of the hopping integrals show a substantial degree of dependence
on the endgroups' conformation, suggesting a significant coupling to the
electronic degrees of freedom. Our findings support the possibility that the
glassy freezing of the ethylene endgroups could drive or enhance glassy charge
dynamics.
