MODELING THE AMORPHOUS PHASE AND THE FOLD SURFACE OF A SEMI-CRYSTALLINE POLYMER - THE GAMBLERS-RUIN METHOD
MODELING THE AMORPHOUS PHASE AND THE FOLD SURFACE OF A SEMI-CRYSTALLINE POLYMER - THE GAMBLERS-RUIN METHOD
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DOI：
10.1016/0032-3861(81)90315-3
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发表时间：
1981-01-01
期刊：
影响因子：
4.6
通讯作者：
HOFFMAN, JD
中科院分区：
文献类型：
--
作者：
GUTTMAN, CM;DIMARZIO, EA;HOFFMAN, JD
具有片层形态的半晶聚合物由非晶区和结晶区交替组成。如果足够长，这个系统中的每个分子都可以穿过结晶区和非晶态区。无定形部分由分子的部分组成，这些部分形成环，在离出现点一定距离的地方重新进入相同的片层，以及在两个不同的晶体片层之间形成连接的桥。（紧褶不被认为是一个环）。圆环和桥的统计与数理统计中的经典赌徒破产问题相同。这是一个有用的观察，因为关于赌徒破产问题的大量现有文献允许我们立即将结果转录到聚合物体系中。利用这种方法，回路数与桥数之比确定为M，即单位统计步长非晶区的厚度。此外，对于三维的简单立方晶格，组成非晶运行的平均步数被确定为3M+ 1。这种模型导致了在半结晶聚合物紧密折叠中涉及的最小晶茎比例的计算。对于一个简单的三次晶格，这是2 3。讨论了熔体中晶体结构和链刚度对该边界的影响。
A semicrystalline polymer with lamellar morphology consists of alternating amorphous and crystalline regions. If sufficiently long, each molecule in this system traverses both the crystalline and amorphous zones. The amorphous portion is comprised of portions of a molecule that form loops that re-enter the same lamella at some distance from the point of emergence, and bridges that form connections between two different crystal lamellae.(A tight fold is not considered to be a loop). The statistics of loops and bridges are shown to be identical to the classical Gambler's Ruin problem in mathematical statistics. This is a useful observation because the extensive existing literature on the Gambler's Ruin problem allows us immediately to transcribe results to the polymer system. Using this approach, the ratio of the number of loops to the number of bridges is determined to be M, the thickness of the amorphous zone in unit statistical steps. Also, the average number of steps comprising the amorphous run is determined to be 3M+ 1 for a simple cubic lattice in three dimensions. This modelling leads to a calculation of the minimal fraction of crystal stems involved in tight folding in a semicrystalline polymer. For a simple cubic lattice this is found to be 2 3. The effects of crystal structure and stiffness of the chain in the melt on this bound are discussed.