在隨機摻入不同數量的甲基(methyl group)在對排聚苯乙烯(syndiotactic polystyrene, sPS)的苯環間位或對位上(3- 及 4-甲基苯乙烯)當作共聚單元後，我們研究了共聚單元/結構對結晶形為以及平衡熔點(Tm0)下降的影響。在熔融結晶(melt-crystallization)下，寬角度X光散射(WAXS)圖譜顯示出對排聚苯乙烯-3甲基苯乙烯(sPS-3MS)的樣品在11 mol%的3MS含量內主要形成β相結晶，而在更高的含量下則是主要形成α相結晶(21 mol%)。在對排聚苯乙烯-4甲基苯乙烯(sPS-4MS)的系統下，只有2 mol% 4MS含量的樣品才會形成以β相為主的結晶，在更高含量下(5 及10 mol%)皆是形成以α相為主的結晶。在冷結晶(cold-crystallization)下，sPS-3MS及sPS-4MS樣品皆形成α相為主的結晶。這兩種無規共聚物皆顯現出偏好形成α相結晶的傾向。在寬角度X光散射的圖譜中，無規共聚物的結晶特徵峰位置普遍有往低q值偏移的現象，且偏移程度會隨著共聚單元的含量增加而提高，代表這些無規共聚物的結晶有較大的晶格常數(除了sPS-4MS的β結晶相)。因此認為這些共聚單元會被併入sPS-3MS及sPS-4MS的α相結晶結構及sPS-3MS的β相結晶結構中，但被排除在sPS-4MS的β相結晶結構外。分子力學(molecular mechanics)的計算結果顯示，結晶的堆積能量(packing energy)會隨著併入更多的共聚單元而升高，尤其在sPS-4MS的β相結構中能量提高更為明顯。因此對於sPS-4MS系統中顯著抑制β相結晶的現象可以簡單歸因於突出的4-甲基基團造成鏈間的堆積能量強烈增加；而此空間排斥力(steric repulsion)在sPS-3MS的β結晶結構中則相對較弱，與在較高的3MS含量才會傾向形成α結晶相的結果一致。
接著利用同步的原位小角度/寬角度X光散射(in-situ SAXS/WAXS)來觀察升溫過程中其晶相的變化。由寬角度X光散射圖譜得知，對於sPS-3MS及sPS-4MS中的α或β相為主的結晶，在升溫過程中皆表現出這些結晶逐漸熔化的行為，過程中並沒有特定結晶相的形成。藉由半徑具有多分散性(polydispersity)的圓柱形形狀因子(form factor)來分析小角度X光散射的升溫圖譜可以得到晶板厚度(lamellar thickness, lc)與溫度的關係，再根據這兩者的關係可以建立Gibbs-Thomson的平衡熔化線(equilibrium melting line)，而平衡熔點(Tm0)可經由外插平衡熔化線到晶板無限厚的情況得到。大致上α與β結晶相的平衡熔點皆隨著共聚單元的含量增加而降低，且在相同系統及濃度下的β相平衡熔點(5及11 mol%的3MS含量及2 mol%的4MS含量)皆高於其對應的α相平衡熔點，表示β相結構仍維持是熱力學穩定的結構。利用Sanchez-Eby理論來描述平衡熔點下降的情況，結果指出不論是sPS-3MS或sPS-4MS的系統，在β相結構中併入甲基皆會比在α相結構中併入甲基有更高的懲罰能量(penalty energy)，意味著併入甲基使β相變得較不穩定的程度會比α相來得大，進而偏好α結晶相的生成。比較sPS-3MS與sPS-4MS的β相結構，併入4MS單元到結構中會比併入3MS有更大的懲罰能量；而對於α相結構，併入3MS單元到結構中會比4MS有更大的懲罰能量。因此，在併入共聚單元到結晶結構後不但會影響結構的能量也會降低其平衡熔點，這改變了過冷 (supercooling)的參考位置也進一步使sPS-3MS與sPS-4MS偏好形成α結晶相。

By incorporating different levels of methyl groups at meta- or para-positions (3- vs. 4-methylstyrene) as comonomer units into syndiotactic polystyrene (sPS), we examined effects of comonomer structure/content on the polymorphic behavior and also the equilibrium melting temperature (Tm0) depression. Upon melt-crystallization, wide-angle X-ray scattering (WAXS) profiles revealed that, syndiotactic poly(styrene-stat-3-methylstyrene) (sPS-3MS) formed predominantly β-crystals for 3MS content up to 11 mol%, followed by dominance of α-crystals at a higher 3MS level (21 mol%); in the case of syndiotactic poly(styrene-stat-4-methylstyrene) (sPS-4MS), predominant formation of β-crystals occurs only at 2 mol% 4MS content, followed by dominance of α-crystals at higher comonomer levels (5 and 10 mol%). Upon cold-crystallization, both sPS-3MS and sPS-4MS consistently gave only α-crystals. It appears that the formation of α-phase is consistently preferred in these random copolymers. WAXS profiles showed that the characteristic reflections generally shift to lower q-positions with increasing comonomer content, i.e., crystals in copolymers have greater unit cell parameters, except for the β-structure of sPS-4MS. Hence, comonomer units are believed to be incorporated into α-crystals in both sPS-3MS and sPS-4MS or β-structure in sPS-3MS, but fully excluded from the β-structure of sPS-4MS. Results of molecular mechanics computation showed that the packing energy increases upon incorporation of comonomer units, the effect being particularly strong for β-crystals of sPS-4MS. The significantly suppressed formation of β-crystals in sPS-4MS may thus be simply attributed to the strongly increased interchain packing energy due to the protruding 4-methyl groups; this steric repulsion is weaker for β-crystals in the sPS-3MS series, consistent with the delayed preference of α-crystals to higher 3MS contents.
Simultaneous small-/wide-angle X-ray scattering (SAXS/WAXS) was used to investigate the polymorphic evolutions upon heating. The WAXS profiles showed that the α- or β-dominated crystals in sPS-3MS and sPS-4MS all consistently gave melting behavior until melting without forming specific crystalline phase. By analyzing the corresponding SAXS heating profiles with polyradius cylinder shape form factor model, the correlations between the lamellar thickness (lc) and temperature can be identified; thus, the Tm0 can be determined via constructing the Gibbs-Thomson equilibrium melting line and extrapolating to the case of infinite lamellar thickness. Generally, the Tm0 of α- and β-crystals were all decrease with increasing comonomer content and the Tm0 of β-crystals (5 and 11 mol% 3MS content and 2 mol% 4MS content) were always higher than that of α-counterpart, indicating that the β-phase remains the thermodynamically stable structure. Besides, the level of Tm0 depression was interpreted by Sanchez-Eby theory, giving that incorporation the methyl groups into the β-structures has higher penalty energy value than into the α-structures in both sPS-3MS and sPS-4MS cases, suggesting that incorporating the methyl groups primarily destabilizes the β-crystals more and further leads to having the preference of the α-crystals formation. Comparing the β-crystals between sPS-3MS and sPS-4MS system, the penalty energy for incorporating 4MS units into the crystal lattice is larger than that of 3MS units; for the α-crystals, the penalty energy value for incorporating 3MS units is larger than that of 4MS units. Thus, incorporating the comonomer units into the crystals will not only elevate the structure energy but also suppress the Tm0, which changes the reference of supercooling and makes sPS-3MS and sPS-4MS have the preference of α-crystal formation.

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