Fig 1 Optical micrograph under E=0.6kV/mm (100×)	Fig 2 Optical micrograph under E=1.0kV/mm (100×)
Fig 3 Optical micrograph under E=2.5kV/mm (100×)	Fig 4 Optical micrograph under E=5.0kV/mm (100×)
Fig 5 Optical micrograph under after 3 days

2. RESULTS AND DISCUSSIONS
2.1 Structure relexation of the ER fluid 
Fig. 1-4 are the pictures of the ER fluid under a series of increased eclectric field (0-5 kV/mm) at room temperature by optical microscope, showing the development of the electric-field-induced structure in the ER system. Two critical points, E_c1 (0.6 kV/mm) and E_c2 (2.5 kV/mm), were found during the process. When E>Ec1, the ER system began to form column structure in some degree(Fig. 3). These single columns changed slightly with the increased field but reformed and adjusted rapidly and formed a high order structure when E reached E_c2, as shown in Fig. 4. After that, the structure didn't change up to E = 5 kV/mm.
    Once formed, the high order structure was very stable even without electric field at all for a long time(>3days, Fig. 5). So, this kind of ER system is considered having strong relaxation in its geometry structure. And this unique character affords the basement for the new testing method SEF.
2.2 Quantitative study of Ec
We tested the relationship of E vs t s using the classic method. The results were shown by the "§" curves in Fig. 6. The range of electric field is 0-5 kV/mm. Two threshold fields were observed, E_c1 (0.6 kV/mm) and E_c2 (2.5 kV/mm).
    Under the same condition, we switched to the new method SEF also showed the results in Fig. 6 ("^." curve). The saturated field is 5 kV/mm. Obvisouly, the curve is pretty smooth and no any critic point, and this curve is basically similar to the theoretical one.
    To make it more clearer, the difference between the two methods were shown in Fig. 7 [ Dts=ts(SEF) -ts(classic)]. From Fig. 7, when E_c1<E<E_c2, the range Dts of is between 24 - 51 Pa and its average is about 36 Pa (Considering the corresponding range of E (~ 2 kV/mm), the change of Dts is very small). We noticed that this average value is almost equal to the value of ts(classic) under E_c1(35 Pa). When E>E_c2, Dts= 0, which means no difference between the two methods at that time.
    Why E_c1 and E_c2 appeared in "classic method" while not in "SEF" for the same ER system? In "SEF", when the saturated field (5 kV/mm) added, as proved above, the system formed a high order structure and especially, very stable(strong relaxation). Then when the field was changed to the proposed value, the system could keep the same high order and stable structure. In another word, the system had finished a phase transition (or proximately) before the testing. So, the electric energy received by the system could be completely used to induce the "fixed" dipoles in stead of "waste" a part of it to overcome the Brown random moving of particles as in the classic method. Under this condition, we can conclude that the ER effect and electric field have a simple one to one relationship in SEF. Thus the factor of K in R. Tao's equation can be omitted and a single continuous function was got, in which no position for E_c1 and E_c2 like in "PCM" model.
    Now the reason that Ec appeared in "classic method" becomes clear: when E<E_c1, the electric energy is relatively small compared to the thermal energy and can not induced any order structure and no any ER effect observed as a result. When E_c1<E<E_c2, the electric energy increased but only in the same level with the thermal energy, the degree of the induced structure is pretty low and far from perfect. There are lots of "voids" in the catenarian (or column) structure. So the electric energy added could be only partly changed into the "useful" dipolarization energy, and efficiency of the induced ER effect is lower than that of "SEF", in which the efficiency is near 100%. The lost part of the efficiency is believed to be dispersed in the void areas, in which Brown thermal random moving dominates, so the difference ER effect for the two methods, can properly reflect how much the thermal energy affects the ER effect. On the other hand, if we reexam the curve of E vs t s in the range of E_c1 - E_c2 in classic method from this point, the ER effect totally comes from order parts and those voids contribute nothing, we can guess this part of line in Fig. 6 is also obey the same rule as the other part(E>E_c2) or the whole line for SEF and only different in a factor, for example, t s µ AE² , but this prediction needs a further detail study to be proved. When E>E_c2, electric energy is the dominant one and the high order structure formed, and the difference of the two methods disappeared naturally.

	Fig 6 ts-E relationship curves by two methode
	Fig 7 The relationship curve of Dts-E

Predictably, the relationship of circuit density I and electric field E has the similar trend under the two testing methods. The results showed it was and consistent with the above analysis. (Fig. 8)

Fig 8  The relationship curve of Dt-E

    The order geometry structure (chain structure) is the bridge for electric energy to induce ER effect. And the structure more perfect, the higher efficiency of the energy is. Additionally, the structure itself doesn't increase the viscosity of the system, which is shown by the results under zero field in two testing methods.
    The dash line in Fig. 6 is theoretical calculation from PCM model. Under relatively low field (E<E_c2), the results from SEF fitted PCM better than those from classic method. But this does not mean that the PTM model is wrong. The consideration of thermal factor K by R. Tao et al is reasonable and necessary. Indeed, it is the competetion between k and other factor, electric U, that causes the exist of E_c1 and E_c2. The two models are both backed by some experimental results. Which one is really right? Or what's their application and limitation? Here we try to give some explanations.
(1) They are both reasonable under specific conditions.
(2) To match an experimental result to one theroy is determined by the comprehensive effect of several factors, such as testing method, range of electric field and the relaxation of ER system, etc.
(3) When the system has strong relaxation, as shown in the present paper, the effect of testing method and range of electric field is listed in Table 1.

2.3 Computer Simulation    
We used Monta Carlo method to simulate the ER fluid based on R. Tao's phase transition model. Here we only give out some results about E_c1 and E_c2.
    When j, the order parameter which indicate the relative value between electric energy and thermal energy, increased from 1 to 5 step by step. We found,
    When j <1.5, no any struture in the system.
    When j =1.5 or higher but smaller than 4.5, single chain structure appeared.
    When j=4.5 or higher, multi-chain struture appeared.
j =1.5 and j =4.5 are two phase transition points and correspond to E_c1 and E_c2, respectively.

3. CONCLUSION
Based on the strong relaxation character of our polyelectrolyte ER system, we study the mechanism of Ec from a new point by designing the "Saturated Electric Field" method. The exist of E_c1 and E_c2 is just because the no structure or not perfect structure in ER system under certain conditions. The structure void causes the ER effect is lower than expected value ( by PCM model) in the field range of E_c1 - E_c2. And this was proved by the successful elimination of E_c1 and E_c2 in the strong relaxtion system tested by SEF. We also made it clear that the applicatin and limitation of two well known models (PCM and PTM) the relationship between our new SEF method and the classic method, which is also probablely useful in ER application in addition to the theoretical value.