We systematically study Raman spectroscopy of cleaved Na$_x$CoO$_2$ single crystals with 0.37 $leq$ x $leq$ 0.80. The Raman shift of A$_{1g}$ mode is found to be linearly dependent on Na content, while the Raman shift of E$_{1g}$ mode has an abnormal shift to high frequency around x = 0.5. The abnormal shift is ascribed to the occurrence of Na rearrangement in O1 structure. Temperature dependent Raman spectrum for x = 0.56 sample shows that Na rearrangement transition from O1 structure to H1 structure occurs around 240 K. Electronic transport and susceptibility for the sample with $x=0.56$ show a response to the Na rearrangement transition from O1 to H1 structure, and that different Na ordering pattern causes distinct physical properties. These results give a direct evidence to proved Na ordering effect on physical properties of Co-O plane.
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