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Tag: viscoelasticity

为什么G”是负值?

主题回归到流变学一下。

众所周知(线性)粘弹性是处于Hookian弹性和Newtonian粘性这两个极端之间的性质。对Hookian弹性体(Hookian弹簧模型)施加正弦形变,测到的是同相的正弦应力;向Newtonian粘流体(Newtonian粘壶)施加正弦形变速率,测到的是同相的正弦应力。向一个线性粘弹性样品施加正弦形变,测到的是相位角为[eq]\delta[/eq]的正弦应力:[eq]\gamma_0 \sin \left ( \omega t+\delta \right )[/eq]

<span lang=zh-CN>小幅振荡力学响应</span>

小幅振荡力学响应

最为人熟悉的流变学测试(也是最多不懂流变的人知道要做的测试)就是[eq]G’[/eq][eq]G”[/eq]~[eq]\omega[/eq]曲线,这个也叫做粘弹谱。我曾经详细解释过[eq]G’[/eq][eq]G”[/eq]到底是怎么来的。典型线型聚合物粘弹谱如下图:

<span lang=zh-CN>线型聚合物粘弹谱</span>

线型聚合物粘弹谱

下图是我配制的合成锂藻土Laponite凝胶的粘弹谱,发现[eq]G”[/eq]在高频处出现负值。下面是对这个不正常现象的解释。

Laponite<span lang=zh-CN>凝胶粘弹谱</span>

Laponite凝胶粘弹谱

一台应变控制型流变仪若要给出这样的图,就要给样品施加一定频率[eq]\omega[/eq]和幅度[eq]\gamma[/eq]的正弦应变[eq]\gamma \left ( t \right ) = \gamma_0 \sin \left ( \omega t \right)[/eq],然后夹具所连接的力学传感器记录样品向夹具施加的转矩,并根据夹具形状和Gap值换算成应变[eq]\sigma \left ( t \right )[/eq],在线性粘弹性条件下[eq]\sigma \left ( t \right )=\sigma_0 \sin \left ( \omega t + \delta \right )[/eq]。仪品仅需且必须准确测量出两个值:[eq]\sigma_0[/eq](从在转矩数据中找到的最值换算)和[eq]\delta[/eq](通过比较转矩数据和应变数据的相位差[eq]\Delta t[/eq]换算,见第1幅图)。其中,[eq]\Delta t=\frac{\delta}{\omega}[/eq]。其他诸如[eq]G’[/eq][eq]\eta’[/eq]之类的,都是从这两个数据算出来的。例如[eq]G”=\frac {\sigma_0}{\gamma_0} \sin \left( \omega \right )[/eq]

如果样品非常接近Hookian弹性体,应力和应变的时间曲线接近同相,相位角[eq]\delta[/eq]的值是非常小的,如果同时频率[eq]\omega[/eq]的值很大,那么相位差[eq]\Delta t[/eq]的值就会非常小。按照第一幅图的情况,,这么大的时间差就算人也能测得很准。但是,在Laponite凝胶粘弹谱中,样品在高频区非常接近Hookian行为,[eq]\delta[/eq]小于,这时,如果要求仪器仍然把[eq]\delta[/eq]测准,就等于要求准确分辨小于万分之几秒的时间差。以为例:

仪器是通过比较应力和应变两条曲线在横轴上的位值差来获得[eq]\Delta t[/eq]的。理论上[eq]\Delta t[/eq]再小也总大于0。但如果待测值小于仪器误差,仪器可能就搞不清两条曲线谁前谁后了,就会出现负值的[eq]\Delta t[/eq],从而出现负值的[eq]\delta[/eq]。虽然[eq]\delta[/eq]出现负值,但绝对值总之并不会太大,所以[eq]\delta[/eq]在第四象限,[eq]\cos\left(\delta\right)\gg 0,\sin\left(\delta\right)<0[/eq],所以遭殃的就会是[eq]G”[/eq]

总之,[eq]G”<0[/eq]的实质是,Hookian样品损耗角[eq]\delta[/eq]的高频值已超过仪器的测量能力,测出来的值不管是正是负,都在误差范围内,已经不可靠了。

How does Google suggests for “rheology”?

Study showed recently that Google search sug­ges­tions may be mis­lead­ing. The study took the word “nan­otech­nol­ogy” for exam­ple and showed that Google fre­quently directs searcher of this word to topic of health impact of nan­otech­nol­ogy. News reporters said this means that Google may scram­ble our per­cep­tion of sci­ence reality.

Although I don’t buy the logic that not know­ing any topic about the health impact of nan­otech­nol­ogy at all is help­ful for a pos­i­tive pub­lic image of nan­otech­nol­ogy, I am still inter­ested what Google sug­gests for “rhe­ol­ogy”. There is a rel­a­tively new tool in Google search — the won­der wheel. When search­ing for “rhe­ol­ogy”, you can start a won­der wheel of it and explore the second-order wheel of each sug­ges­tion to “rheology”.

wonder wheel.jpg

To my sur­prise, “thixotropic” seems much more sug­gestible than “vis­coelas­tic”. Does this mean peo­ple want to know about the for­mer more fre­quently than the lat­ter? Also more sug­gestible than “vis­coelas­tic” is the sim­pler con­cept “vis­cos­ity”. “Viscoelastic” is even not in the sug­ges­tion list.

“Viscoelastic” does appears in wider list of sug­ges­tion, though.

related searches.jpg

Viscoelasticity is a fun­da­men­tal con­cept in rhe­ol­ogy. The study of this prop­erty started from the very begin­ning of the his­tory of rhe­ol­ogy until today. However, many that are new to rhe­ol­ogy find it much harder to accept than the con­cept of vis­cos­ity or even thixotropy.

The con­cept of vis­cos­ity is sim­ple. The famous Newtonian def­i­n­i­tion appears exclu­sively in every text­books. And start­ing from this, it is quite easy to under­stand what is non-Newtonian. Indeed, the Newtoinan/non-Newtonian type of clas­si­fi­ca­tion is very con­ve­nient for flu­ids — things that can flow, but most rhe­o­log­i­cal prob­lems is con­cerned by things with flu­id­ity that depends. The abyss most stu­dents of rhe­ol­ogy really strug­gling against is things that can­not be prop­erly char­ac­ter­ized by only vis­cos­ity but need to intor­duce the mea­sures of G’ and G”. I have been asked too many times about the “real, real mean­ing” of these mod­uli. Even expe­ri­enced mate­ri­als sci­ence researchers may not under­stand why bother uses this com­pli­cated frame­work of mea­sure to char­ac­ter­ize a piece material.

No bother indeed, in the prac­ti­cal con­text. There are two rheome­ters in my research group. Colleagues from other col­lages or insti­tutes often find me for rheom­e­try. 90% of the cases are requests for sim­ple vis­cos­ity vs shear rate curves. Only when a requester wants to “add more plots and depth” to his/her paper would he/she asked for dynamic, that is, G’/_G_” tests. In indus­try, a vis­cos­ity curve gives enough infor­ma­tion for pro­duc­tion in most cases.

The also pop­u­lar “thixotropy” should thank the indus­try, too. Thixotropy is hard to char­ac­ter­ize in a sci­en­tific way (ready for struc­tural mod­el­ing) till even today, but mate­ri­als of this prop­erty are essen­tial for the exis­tence of the paint indus­try, where an ad hoc thixotropic loop test is enough in most cases. More inter­est­ingly, while the con­cept of vis­cos­ity can­not meet the cases where the flu­id­ity of mate­ri­als is depen­dent, the con­cept of thixotropy is just about the dual­ity of “flow/don’t flow”, some­what com­ple­ment­ing the for­mer. In the prac­ti­cal sense, it seems that sim­ple extreme con­cept like flow and not-flow (i.e. Newtonian vs Hookian) is enough in deal­ing rhe­o­log­i­cal prob­lems. That’s why Google does not sug­gest “vis­coelas­tic” when searched for “rhe­ol­ogy”. This may be mis­lead­ing, how­ever, when the user wants to know about rhe­ol­ogy academically.

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