Dimensions of Polymer Chains in Critical Semidilute Solutions

Mel’nichenko, Yu. B.; Wignall, G. D.

doi:10.1103/physrevlett.78.686

Cited by 49 publications

(79 citation statements)

References 19 publications

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“…2, the same crossover is manifested by the correlation length. It is remarkable that the correlation length taken at the crossover temperature follows almost perfectly the normalized radius of gyration R g / √ 3, independently measured by neutron scattering [21]. It also follows from our analysis that the dependence of the critical amplitudes on the molecular weight can be described within experimental accuracy by de Gennes' scaling [6,22].…”

supporting

confidence: 76%

Competition of mesoscales and crossover to tricriticality in polymer solutions

2002

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We show that the approach to asymptotic fluctuation-induced critical behavior in polymer solutions is governed by a competition between a correlation length diverging at the critical point and an additional mesoscopic length-scale, the radius of gyration. Accurate light-scattering experiments on polystyrene solutions in cyclohexane with polymer molecular weights ranging from 200,000 up to 11.4 million clearly demonstrate a crossover between two universal regimes: a regime with Ising asymptotic critical behavior, where the correlation length prevails, and a regime with tricritical theta-point behavior determined by a mesoscopic polymer-chain length. PACS: 64.75.+g; 61.25.Hg; 05.70.Jk Close enough to the critical point, the correlation length ξ of the fluctuations of the order parameter has grown so large that the microscopic and even the mesoscopic structure of fluids become unimportant: complex fluids become "simple". This feature is known as criticalpoint universality [1]. Within a universality class, determined by the nature of the order parameter, properly chosen physical properties of different systems exhibit the same near-critical behavior. All critical phase-separation transitions in fluids belong to the 3-dimensional Isingmodel universality class, as the order parameter (associated with density or/and concentration) is a scalar. However, in practice, the pure asymptotic regime is often hardly accessible. Even in simple fluids, like xenon and helium, the physical properties in the critical region show a tendency to crossover from Ising asymptotic behavior to mean-field behavior [2,3]. This crossover depends on the microscopic structure of the system, namely, on the range of interaction and on a molecular-size "cutoff". In simple fluids, crossover to mean-field critical behavior is never completed within the critical domain (which can be defined roughly as within 10% of the critical temperature): the "cutoff" length and the range of interactions are too short. In complex fluids, regardless of the range of interaction, the role of the cutoff is played by a mesoscopic characteristic length scale ξ D that is associated with a particular mesoscopic structure [4]. If the cutoff length is mesoscopic, it can compete with the correlation length ξ within the critical domain. The temperature at which the correlation length becomes equal to the structural length can be naturally defined as a crossover temperature between two regimes, namely, an Ising asymptotic critical regime and a regime determined by the nature of the mesoscopic structure of the complex fluid. In some complex fluids, like polymer solutions, it is possible to tune the structural length-scale and make it very large. If both lengths, the correlation length of the critical fluctuations associated with the fluid-fluid separation and the structural correlation length, diverge at the same point, this point will be a multicritical point. A perfect example of such a multicritical phenomenon appears in a polymer solution near the theta point. The theta p...

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supporting

confidence: 76%

Competition of mesoscales and crossover to tricriticality in polymer solutions

2002

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“…For polystyrene ͑PS͒ in cyclohexane ͑CH͒, recent experiments indicate that the chains are not collapsed near the critical point; 36 however, for poly͑␣-methylstyrene͒ in cyclohexane, significant contraction of the chains is observed 37 for TϽ⌰. It is to be noted that the coil-to-globule transition has been observed for subtheta solutions of PS in CH at concentrations far below the critical point, 38,39 and by quenching into the twophase region.…”

Section: Analytic Thread Prism Theory For Homopolymer Fluids Witmentioning

confidence: 96%

Analytic integral equation theory for the critical properties of homopolymer fluids

Chatterjee

Schweizer

1998

The Journal of Chemical Physics

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We apply the analytic version of the polymer reference interaction site model theory to determine the critical properties of homopolymer fluids. The Gaussian thread model is used throughout, together with a Yukawa form for the attractive interaction between chain segments. Atomiclike as well as molecular closures are employed, and results are presented using both the compressibility and free-energy route approaches to the thermodynamics. Predictions derived based on different closure approximations for the chain length (N) dependence of the theta and critical temperatures, and of the critical density, are compared with the results of simulations of the liquid-vapor equilibrium in homopolymer systems, as well as with experimental results for the demixing transition in polymer solutions. The large N asymptotic scaling laws, and finite size corrections, for the critical properties depend strongly on the closure employed for treating attractive interactions, and for all cases studied significant deviations from the mean-field Flory-Huggins lattice theory are found. The importance of simultaneously including fluctuation effects associated with both the repulsive and attractive interactions is demonstrated. Model calculations are also presented for the liquid-vapor spinodal and coexistence curves.

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“…The pre-transition step involves PNIPAM chain shrinking while the transition itself involves complete demixing driven by chi effects. Note that another experiment used SANS with the zero average contrast method to investigate single-chain polymer conformation of polystyrene in cyclohexane [14] at the critical composition. They found very small chain contraction as evidenced by a very slight decrease in the single-chain radius of gyration.…”

Section: Summary and Discussionmentioning

confidence: 99%

Single-Chain Conformation for Interacting Poly(N-isopropylacrylamide) in Aqueous Solution

Hammouda

Di²,

Cheng

2015

The Open Access Journal of Science and Technology

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Abstract. The demixing phase behavior of Poly(N-isopropylacrylamide) (PNIPAM) aqueous solution is investigated using smallangle neutron scattering. This polymer phase separates upon heating and demixes around 32 ∘ C. The pre-transition temperature range is characterized by two scattering modes; a low-Q (large-scale) signal and a high-Q dissolved chains signal. In order to get insight into this pre-transition region, especially the origin of the low-Q (large-scale) structure, the zero average contrast method is used in order to isolate single-chain conformations even in the demixing polymers transition region. This method consists of measuring deuterated and non-deuterated polymers dissolved in mixtures of deuterated and non-deuterated water for which the polymer scattering length density matches the solvent scattering length density. A fixed 4% polymer mass fraction is used in a contrast variation series where the d-water/h-water fraction is varied in order to determine the match point. The zero average contrast (match point) sample displays pure single-chain scattering with no interchain contributions. Our measurements prove that the large scale structure in this polymer solution is due to a transient polymer network formed through hydrophobic segmentsegment interactions. Scattering intensity increases when the temperature gets close to the phase boundary. While the apparent radius of gyration increases substantially at the Lower Critical Solution Temperature (LCST) transition due to strong interchain correlation, the single-chain true radius of gyration has been found to decrease slightly with temperature when approaching the transition.

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Dimensions of Polymer Chains in Critical Semidilute Solutions

Cited by 49 publications

References 19 publications

Competition of mesoscales and crossover to tricriticality in polymer solutions

Competition of mesoscales and crossover to tricriticality in polymer solutions

Analytic integral equation theory for the critical properties of homopolymer fluids

Single-Chain Conformation for Interacting Poly(N-isopropylacrylamide) in Aqueous Solution

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