Four gemini cationic surfactants {N,N′-di[2-(lauryldimethylamino)acetyl]polymethylenediamine dichloride, LAA-s-LAA, s=2,3,4,6} were synthesized by using four bis(α-chloroacetamide)s and N,N-dimethyllaurylamine, resp...Four gemini cationic surfactants {N,N′-di[2-(lauryldimethylamino)acetyl]polymethylenediamine dichloride, LAA-s-LAA, s=2,3,4,6} were synthesized by using four bis(α-chloroacetamide)s and N,N-dimethyllaurylamine, respectively. The molecular structures were characterized by means of IR, ~ 1H NMR, \{~ ~13 C NMR\} and MS, and the behavior of their aqueous solutions was studied. The critical micell concentrations(CMC) of LAA-s-LAA were one order of magnitude lower than that of dodecyltrimethyl ammonium chloride(DTAC). With the change of the length of spacer chain(s), their CMC values change, and CMC reaches the top value at s=4.展开更多
We re-derive exactly the transverse Ward–Takahashi relation for the vector vertex in momentum space. The result shows that this transverse Ward–Takahashi relation in momentum space involves a perturbative correction...We re-derive exactly the transverse Ward–Takahashi relation for the vector vertex in momentum space. The result shows that this transverse Ward–Takahashi relation in momentum space involves a perturbative correction term. We demonstrate explicitly that this transverse Ward–Takahashi relation is satisfied indeed at one-loop order.展开更多
文摘Four gemini cationic surfactants {N,N′-di[2-(lauryldimethylamino)acetyl]polymethylenediamine dichloride, LAA-s-LAA, s=2,3,4,6} were synthesized by using four bis(α-chloroacetamide)s and N,N-dimethyllaurylamine, respectively. The molecular structures were characterized by means of IR, ~ 1H NMR, \{~ ~13 C NMR\} and MS, and the behavior of their aqueous solutions was studied. The critical micell concentrations(CMC) of LAA-s-LAA were one order of magnitude lower than that of dodecyltrimethyl ammonium chloride(DTAC). With the change of the length of spacer chain(s), their CMC values change, and CMC reaches the top value at s=4.
文摘We re-derive exactly the transverse Ward–Takahashi relation for the vector vertex in momentum space. The result shows that this transverse Ward–Takahashi relation in momentum space involves a perturbative correction term. We demonstrate explicitly that this transverse Ward–Takahashi relation is satisfied indeed at one-loop order.
