The internal modes of polystyrene single coils studied using dynamic light scattering

Nicolai, Taco; Brown, Wyn; Johnsen, Robert M.

doi:10.1021/ma00196a045

Cited by 25 publications

(20 citation statements)

References 12 publications

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“…In the past decades, numerous efforts have been devoted to the understanding of internal dynamics for linear chains. − In related studies, the main focuses are the scaling behavior of the first cumulant [Γ( q )], the asymptotic behavior of the reduced first cumulant (Γ* = [η 0 Γ( q )/( k B Tq 3 )]), and the characteristic relaxation time (τ 1 ) of the first internal mode, where η 0 is the solvent viscosity, and a qualitatively satisfying agreement has been achieved between experimental findings and theoretical predictions. − …”

Section: Introductionmentioning

confidence: 92%

Light Scattering Study of Internal Motions of Ultralong Comb-like Chains in Dilute Solutions under Good Solvent Conditions

et al. 2020

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Internal dynamics of polymer chains is one of the most important fundamental problems in polymer physics. This work reports the first example of a dynamic light scattering (DLS) study of internal motions of well-defined ultralong comb-like chains in dilute solutions under good solvent conditions. Using two well-characterized comb-like model samples with controlled parameters and narrow distributions (M w /M n ≈ 1.30 and M w ≈ 10 7 g/mol), the asymptotic behavior of the reduced first cumulant [Γ* = Γ(q)/(q 3 k B T/ η 0 )], the number of relaxation modes in Γ(q) distribution curves, the characteristic relaxation time (τ 1 ) of the first internal mode, and the q-dependent relative strength of internal motions have been experimentally quantified and carefully analyzed where q is the scattering vector. Specifically, the DLS results reveal the following: (i) Γ*(q ≫ 1), that is, the value of Γ* at the very high q regime, is not sensitive to structural details (local rigidity and side chain length); (ii) similar to hyperbranched polymers, the asymptotic power law in the regime of 3.0 < (q⟨R g ⟩) < 5.5 is also found to be a better indicator, which could reflect the structural details for comb-like polymers; (iii) the comparison of experimentally determined and theoretically calculated values of τ 1 shows that the classical theory of linear chains could still satisfactorily describe the intrachain relaxation behavior of comb-like chains; and (iv) the side-chain grafting-induced rigidity could result in an enhanced separation of translational and internal motions but simultaneously result in a significant suppression of the strength of overall internal motions. The present study not only reveals that the modes of internal motions of a given system are mainly determined by the relaxation of the main contour of a given chain structure rather than the local chain rigidity but also provides useful experimental data for further theoretical modeling of internal dynamics of various topological polymers.

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Section: Introductionmentioning

confidence: 92%

Light Scattering Study of Internal Motions of Ultralong Comb-like Chains in Dilute Solutions under Good Solvent Conditions

et al. 2020

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“…[8][9][10] A combination of the line-width distributions G(Γ) of narrowly distributed flexible long polymer chains, respectively, measured at a small and a high angle allows us to experimentally separate the translational and internal motions. 11 More quantitatively, when a coherent and monochromatic laser beam hits a dilute solution of linear flexible polymer chains without any adsorption, the scattered light has a spectral distribution, S(q,ω), due to the translational diffusion and internal motions as follows. 12 Sðq, ωÞ ¼ ð1=2πÞ…”

Section: Introductionmentioning

confidence: 99%

Internal Motions of Linear Chains and Spherical Microgels in Θ and Poor Solvents

Dai

2010

Macromolecules

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Internal motions of narrowly poly(N-isopropylacrylamide) (PNIPAM) linear chains and spherical microgels in a very dilute aqueous solution and dispersion were studied under the Θ and poor solvent conditions by dynamic laser light scattering (LLS) over a wide range of scattering angles. As expected, only one narrow peak related to the translational diffusion was observed in the line-width distribution G(Γ) of both linear chains and spherical microgels when x < 1, where x = (qR g ) 2 with q and R g the scattering vector and the radius of gyration, respectively. As x increases to approach 1, we start to see a second peak related to fast internal motions of linear chains, whose average line width is related to some of the internal motions (normal modes) predicted in the nondraining bead-and-spring model. However, for swollen microgels, the second peak related to the internal motions only appears when x is much higher (1/q ∼ 50 nm), indicating that thermal energy is not able to excite the entire microgel but only a small portion of the gel network. As the solvent quality changes from good to poor, the shrinking of a linear chain or subchains in the gel network gradually suppresses the internal motions, presumably due to stronger intersegment interaction. Surprisingly, we found that the relative contribution of the second peak makes a turning near the Θ temperature, leading to a new way to estimate the Θ condition of a given polymer solution.

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“…Since there is some controversy concerning the correct value for AI, it is preferable to base discussion on experimentally determined quantities. Recent investigations [120,121] have confirmed the value of 1.2 in theta-solvents. From the spectrum of scattered light, different methods of analysis have been applied to estimate fl for comparison with the theoretical predictions [119][120][121].…”

Section: End-to-end Chain Relaxation Timementioning

confidence: 68%

“…Predicted respectively by Rouse [113) and Zimm [114] in the limits of free draining and nonfree draining bead-spring chains, fl can be conveniently expressed in the form [115]: (8.29) The numerical factor Al is 0.822 for the free draining chain [113],1.184 for the non-free draining chain with pre-averaged hydrodynamic interactions [114,116] and 0.574 without preaveraging the Oseen tensor [117]. From the spectrum of scattered light, different methods of analysis have been applied to estimate fl for comparison with the theoretical predictions [119][120][121]. Since there is some controversy concerning the correct value for AI, it is preferable to base discussion on experimentally determined quantities.…”

Section: End-to-end Chain Relaxation Timementioning

confidence: 99%

“…Dynamic light scattering is a technique frequently used for probing the internal motions of flexible polymer chains in solution. In ethyl-benzene, a good solvent for PS, a smaller value of Al = 0.84 has been obtained [121]. In some studies, it has been found that PS at infinite dilution, either in good (benzene) or theta (trans-decalin) solvents, behaves according to the Zimm model with Al ~ 1.2 [115,119].…”

Section: End-to-end Chain Relaxation Timementioning

confidence: 99%

See 1 more Smart Citation

Flexible Polymer Chains in Elongational Flow

Nguyen¹,

Kausch²

1999

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The internal modes of polystyrene single coils studied using dynamic light scattering

Cited by 25 publications

References 12 publications

Light Scattering Study of Internal Motions of Ultralong Comb-like Chains in Dilute Solutions under Good Solvent Conditions

Light Scattering Study of Internal Motions of Ultralong Comb-like Chains in Dilute Solutions under Good Solvent Conditions

Internal Motions of Linear Chains and Spherical Microgels in Θ and Poor Solvents

Flexible Polymer Chains in Elongational Flow

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