Surface grafting of polymers onto inorganic ultrafine particles: Reaction of functional polymers with acid anhydride groups introduced onto inorganic ultrafine particles

The surface grafting onto inorganic ultrafine particles, such as silica, titanium oxide, and ferrite, by the reaction of acid anhydride groups on the surfaces with functional polymers having hydroxyl and amino groups was examined. The introduction of acid anhydride groups onto inorganic ultrafine particle was achieved by the reaction of hydroxyl groups on these surfaces with 4-trimethoxysilyltetrahydrophthalic anhydride in toluene. The amount of acid anhydride groups introduced onto the surface of ultrafine silica, titanium oxide, and ferrite was determined to be 0.96, 0.47, and 0.31 mmol/g, respectively, by elemental analysis. Functional polymers having terminal hydroxyl or amino groups, such as diol-type poly(propylene glycol) (PPG), and diamine-type polydimethylsiloxane (SDA), reacted with acid anhydride groups on these ultrafine particles to give polymer-grafted ultrafine particles: PPG and SDA were considered to be grafted onto these surfaces with ester and amide bond, respectively. The percentage of grafting increased with increasing acid anhydride group content of the surface: the percentage of grafting of SDA (M_n = 3.9 × 10³) onto silica, titanium oxide, and ferrite reaching 64.7, 33.7, and 24.1%, respectively. These polymer-grafted ultrafine particles gave a stable colloidal dispersion in organic solvents.     

The crystal structures of α- and β-CdUO4

The structural parameters of α- and β-CdUO₄ crystals are determined by X-ray powder diffraction technique. α-CdUO₄ is rhombohedral and cell parameters are a = 6.233(3) Å and α = 36.12(5)°. β-CdUO₄ crystallizes in a C-centered orthorhombic cell with a = 7.023(4), b = 6.849(3), c = 3.514 (2) Å. The space groups are $\text{R}\text{3}\text{m}$ for α-CdUO₄ and Cmmm for β-CdUO₄. α-CdUO₄: 1U in (000), 1Cd in ($\text{1}\text{2}\text{1}\text{2}\text{1}\text{2}$), 2O(1) in ±(uuu), 2O(2) in ±(vvv); u = 0.113, v = 0.350, Z = 1. β-CdUO₄: 2U in ($\text{000;}\text{1}\text{2}\text{1}\text{2}\text{0}$), 2Cd in ($\text{1}\text{2}\text{0}\text{1}\text{2}\text{; 0}\text{1}\text{2}\text{,}\text{1}\text{2}$), 4O(1) in ($\text{0, ±y, 0;}\text{1}\text{2}\text{,}\text{1}\text{2}\text{±y, 0}$), 4O(2) in ($\text{±x, 0,}\text{1}\text{2}\text{;}\text{1}\text{2}\text{±x,}\text{1}\text{2}\text{,}\text{1}\text{2}$); x = 0.159, y = 0.278, Z = 2. β-CdUO₄ contains collinear uranyl UO²⁺₂ groups with a UO(1) distance of 1.91 Å, located either along or parallel to the c axis whereas the UO(1) bond length in α-CdUO₄ is 1.98 Å which is longer than the usual uranyl bond length.     

Asymptotic behavior of basic contact process with rapid stirring

In this paper we consider the basic contact process with infection rate λ and stirring rateD. We study the asymptotic behavior of the critical value and survival probability asD→∞.