568 ± 0.027 0.668 ± 0.032 1.636 ± 0.078 APEG 600 521 ± 51 0.672 ± 0.054 0.791 ± 0.064 1.938 ± 0.156 APEG 1,000 997 ± 77 0.944 ± 0.025 1.111 ± 0.029 2.721 ± 0.072 APEG 2,000 1,887 ± 20

1.602 ± 0.284 1.885 ± 0.334 4.617 ± 0.818 APEG 4,000 3,981 ± 82 1.784 ± 0.165 2.099 ± 0.194 5.141 ± 0.475 APEG 6,000 6,185 ± 165 2.343 ± 0.111 2.756 ± 0.131 6.751 ± 0.320 APEG 8,000 8,232 ± 162 2.749 ± 0.101 3.234 ± 0.119 7.922 ± 0.291 APEG 10,000 10,535 ± 907 3.306 ± 0.063 3.889 ± 0.074 9.526 ± 0.182 APEG 12,000 13,646 ± 1359 3.522 ± 0.061 4.144 ± 0.072 10.151 ± 0.176 APEG 20,000 19,118 ± 631 4.415 ± 0.015 5.194 ± 0.018 12.723 ± 0.043 SPEG 1,450 1,348 ± 64 1.203 ± 0.097 1.415 ± 0.114 3.466 ± 0.280 SPEG 4,600 VX-689 molecular weight 4,384 ± 436 2.095 ± 0.045 2.465 ± 0.053 6.038 ± 0.130 SPEG 8,000 8,350 ± 301 2.572 ± 0.299 3.026 ± 0.352 7.412 ± 0.862 SPEG 10,000 10,641 ± 219 3.474 ± 0.214 4.087 ± 0.252 10.011 ± 0.617 a M w was determined by MALLS. b R h was determined by DLS. c R g was calculated using Equation 2. d〈h 2〉1/2 was calculated using Equation 3. Since the PEG chains behave much like ideal

chains in water, the R g is related to the 〈h 2〉1/2, which is expressed by the following equation [23, 24]: (3) The data of the above calculations are listed in Table 1. According to the previous reports, a relationship exists between the M w and the R g of PEG, and a linear fit of these variables yields the coefficient υ with the relationship R g ∝ M w υ [23–25]. Moreover, when the M w is low (<80,000 Da), the effects of excluded volume interactions diminish, and υ → 0.5 [23, 25, 26]. When υ = 0.5, a polymer chain behaves in an ideal (Gaussian) selleck manner in a θ solvent [23]. Since the 〈h 2〉1/2 is directly proportional to the R g (Equation 3), 〈h 2〉1/2 ∝ M w υ [24], which is described by (4) with an R 2 = 0.9994. This relationship is presented in Additional file 1: Figure S1 and plotted according to the M w and the mafosfamide 〈h 2〉1/2 values of the PEG samples (APEG 400 to 20,000) listed in Table 1. The coefficient υ is 0.5250,

which is close to 0.5, establishing the fact that the PEG chains behave much like ideal chains in the solution [23]. In order to verify the colorimetric method, two sizes of AuNPs were prepared by reducing HAuCl4 with different amounts of trisodium citrate (see ‘Selleck ICG-001 Methods’). Through TEM examination, the diameters of the as-prepared AuNPs were measured to be about 16 and 26 nm, respectively (Additional file 1: Figure S2).