Conformations of a Long Polymer in a Melt of Shorter Chains: Generalizations of the Flory Theorem

Lang, Michael; Rubinstein, Michael; Sommer, Jens‐Uwe

doi:10.1021/mz500777r

Cited by 32 publications

(47 citation statements)

References 22 publications

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“…The radius of gyration of the RP is about 17% greater in a matrix of N m = 10 compared to N m = 300 LPs. A similar expansion is also observed in binary linear blends, wherein a long probe molecule of molecular weight N l expands when the molecular weight of the shorter matrix polymers decreases below

N_{m}^{†} \sim \sqrt{N_{l}}

. The magnitude of the expansion in the size of the RP, below this threshold, is consistent with the expected

R \sim N_{m}^{- 0.1}

scaling for LPs, as shown in Figure .…”

Section: Resultssupporting

confidence: 80%

“…The magnitude of the expansion in the size of the RP, below this threshold, is consistent with the expected

R \sim N_{m}^{- 0.1}

scaling for LPs, as shown in Figure . Although classical theory suggests a stronger

R \sim N_{m}^{- 0.18}

dependence in this

N_{m} < N_{m}^{†}

regime, experiments, simulations, and a generalized form of the classical theory which includes long‐range bond correlations in melts, and better treatment of excluded volume effects support

R \sim N_{m}^{- 0.1}

…”

Section: Resultsmentioning

confidence: 90%

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Unusual dynamics of ring probes in linear matrices

Shanbhag

2016

J Polym Sci B Polym Phys

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We perform Monte Carlo simulations of ring and linear polymers in linear matrices, and investigate the diffusivity of the probes. As the matrix chain length Nm is increased from 10 to 300 monomers, the diffusivity Dl of a linear probe (Nl = 300) decreases monotonically, while that of a ring probe Dr varies non‐monotonically, with a peak around Nm≈30−75. We perform additional simulations with a single probe molecule ( Nr=Nl=150) in a linear matrix ( Nm=10−150). The non‐monotonicity in Dr persists even after ring–ring interactions are eliminated. Topology dependent differences in the short‐time dynamics of the probes are observed; unlike linear probes, mean‐squared displacements of ring probes depend on Nm. Primitive path analysis suggests that the difference in dynamics originates from differences in entanglement structure. For linear probes, the degree of entanglement is independent of Nm. For ring probes, we observe two regimes: when Nm is small, the number of threadings decreases as Nm increases, eventually transitioning to a plateau. In the small Nm regime, the change in the degree of entanglement offsets the change in the mobility of the matrix chains, leading to a non‐monotonic variation in Dr. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017, 55, 169–177

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N_{m}^{†} \sim \sqrt{N_{l}}

. The magnitude of the expansion in the size of the RP, below this threshold, is consistent with the expected

R \sim N_{m}^{- 0.1}

scaling for LPs, as shown in Figure .…”

Section: Resultssupporting

confidence: 80%

“…The magnitude of the expansion in the size of the RP, below this threshold, is consistent with the expected

R \sim N_{m}^{- 0.1}

scaling for LPs, as shown in Figure . Although classical theory suggests a stronger

R \sim N_{m}^{- 0.18}

dependence in this

N_{m} < N_{m}^{†}

regime, experiments, simulations, and a generalized form of the classical theory which includes long‐range bond correlations in melts, and better treatment of excluded volume effects support

R \sim N_{m}^{- 0.1}

…”

Section: Resultsmentioning

confidence: 90%

Unusual dynamics of ring probes in linear matrices

Shanbhag

2016

J Polym Sci B Polym Phys

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“…It lies in the fact that in the melting process of crystallites, the polymer chains cannot diffuse sufficiently and rapidly to adopt a very different mass distribution from that in the crystalline state. [39][40][41][42] The chain collapse transitions during cooling are also observed in other P3HT/toluene solutions with concentrations ranged from 2.5 to 25 mg ml −1 , as shown in Figure 6 (a). In these solutions, R g of P3HT appears to undergo a similar abrupt drop at a critical temperature during cooling.…”

Section: Resultsmentioning

confidence: 68%

“…Somehow this is not surprising as R g in melt and crystalline states have been widely reported to be the same for many polymers. It lies in the fact that in the melting process of crystallites, the polymer chains cannot diffuse sufficiently and rapidly to adopt a very different mass distribution from that in the crystalline state …”

Section: Resultsmentioning

confidence: 99%

Collapse Transition‐Assisted Crystallization in P3HT Solution

Sun

Zhao

Huang

et al. 2019

J Polym Sci B Polym Phys

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Understanding the multiple phase transitions such as collapse transition, phase separation, and crystallization in solutions is of fundamental importance to control the solution structure of conjugated polymers in device processing. Combining in situ synchrotron radiation small and wide‐angle X‐ray scattering, ultrasensitive differential scanning calorimetry, ultraviolet–visible absorption spectroscopy, and polarized optical microscopy, we investigate the order–disorder transitions in poly(3‐hexylthiophene)/toluene solutions during cooling and heating processes. We demonstrate the occurrence of collapse transition of polymer chains from a random coil state to a lower dimensional network prior to the onset of crystallization during cooling in solution. This conformational preordering can lead to the formation of a lyotropic liquid crystalline phase, which is of great significance to the crystallization and ordering in polymer films, and further to promote its electric performance. It is examined that the mobility of films cast from chain‐collapsed solutions can be one order of magnitude higher than that from isotropic solutions with random‐coiled conformations. Thus, the conformational preordering in solutions is proposed to be a more efficient way than the postannealing of films to improve the electric performance of conjugated polymer films. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019, 57, 1105–1114

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“…The expansion of long chains becomes insignificant as the segment number of shorter chains is larger than a certain value (m1=40). In the early theoretical investigations [9,15], it was predicted that polymer chains (with segment number m) can be expanded in its homologue (with segment number m1) in the range of m1<m1/2. However, these investigations are based on an ideal chains model.…”

Section: Resultsmentioning

confidence: 99%

Density Functional Theory of Polymer Structure and Conformations

et al. 2016

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Abstract:We present a density functional approach to quantitatively evaluate the microscopic conformations of polymer chains with consideration of the effects of chain stiffness, polymer concentration, and short chain molecules. For polystyrene (PS), poly(ethylene oxide) (PEO), and poly(methyl methacrylate) (PMMA) melts with low-polymerization degree, as chain length increases, they display different stretching ratios and show non-universal scaling exponents due to their different chain stiffnesses. In good solvent, increase of PS concentration induces the decline of gyration radius. For PS blends containing short (m 1 " 1´100) and long (m " 100) chains, the expansion of long chains becomes unobvious once m 1 is larger than 40, which is also different to the scaling properties of ideal chain blends.

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Conformations of a Long Polymer in a Melt of Shorter Chains: Generalizations of the Flory Theorem

Cited by 32 publications

References 22 publications

Unusual dynamics of ring probes in linear matrices

Unusual dynamics of ring probes in linear matrices

Collapse Transition‐Assisted Crystallization in P3HT Solution

Density Functional Theory of Polymer Structure and Conformations

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