Department of Polymer Science and Engineering, Faculty of Engineering, Yamagata University, 4-3-16 Jonan, Yonezawa 992-8510, Japan.
J Chem Phys. 2010 Nov 21;133(19):194902. doi: 10.1063/1.3498779.
We have developed a single-chain theory that describes dynamics of associating polymer chains carrying multiple associative groups (or stickers) in the transient network formed by themselves and studied linear viscoelastic properties of this network. It is shown that if the average number N of stickers associated with the network junction per chain is large, the terminal relaxation time τ(A) that is proportional to τ(X)N(2) appears. The time τ(X) is the interval during which an associated sticker goes back to its equilibrium position by one or more dissociation steps. In this lower frequency regime ω<1/τ(X), the moduli are well described in terms of the Rouse model with the longest relaxation time τ(A). The large value of N is realized for chains carrying many stickers whose rate of association with the network junction is much larger than the dissociation rate. This associative Rouse behavior stems from the association/dissociation processes of stickers and is different from the ordinary Rouse behavior in the higher frequency regime, which is originated from the thermal segmental motion between stickers. If N is not large, the dynamic shear moduli are well described in terms of the Maxwell model characterized by a single relaxation time τ(X) in the moderate and lower frequency regimes. Thus, the transition occurs in the viscoelastic relaxation behavior from the Maxwell-type to the Rouse-type in ω<1/τ(X) as N increases. All these results are obtained under the affine deformation assumption for junction points. We also studied the effect of the junction fluctuations from the affine motion on the plateau modulus by introducing the virtual spring for bound stickers. It is shown that the plateau modulus is not affected by the junction fluctuations.
我们提出了一个单链理论，用于描述携带多个关联基团（或“粘性基团”）的聚合物链在由其自身形成的瞬态网络中的动力学，并研究了该网络的线性粘弹性。结果表明，如果每条链与网络结关联的粘性基团的平均数量 N 很大，则会出现与 τ(X)N(2)成正比的末端松弛时间 τ(A)。τ(X)是粘性基团通过一个或多个离解步骤回到平衡位置的时间间隔。在这个较低的频率 ω<1/τ(X)范围内，用具有最长松弛时间 τ(A)的罗瑟模型可以很好地描述模量。对于携带大量粘性基团的链，由于其与网络结的关联速率远大于离解速率，因此可以实现较大的 N 值。这种关联罗瑟行为源于粘性基团的关联/离解过程，与较高频率范围内源于粘性基团之间的热分子运动的普通罗瑟行为不同。如果 N 不是很大，则在中等和较低频率范围内，用由单个松弛时间 τ(X)表征的马克斯韦尔模型可以很好地描述动态剪切模量。因此，随着 N 的增加，在粘弹性松弛行为中从马克斯韦尔类型到罗瑟类型发生转变。所有这些结果都是在对连接点进行仿射变形假设的条件下得到的。我们还通过引入绑定粘性基团的虚拟弹簧，研究了连接点波动对平台模量的影响。结果表明，平台模量不受连接点波动的影响。
