Thermal Patterning of a Critical Polymer Blend

Voit, Albert; Krekhov, A. P.; Enge, W.; Kramer, Lorenz; Köhler, W.

doi:10.1103/physrevlett.94.214501

Cited by 48 publications

(39 citation statements)

References 21 publications

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“…4b). These findings contradict several theoretical studies claiming that D T should be independent of particle size (16)(17)(18)(19)(20)26), based on ambiguous experimental results from thermal field flow fractionation (4) that were probably biased by nonlinear thermodiffusion in large thermal gradients (15).…”

Section: Theoretical Approachcontrasting

confidence: 83%

“…The Soret coefficient is defined as ratio S T ϭ D T /D, which determines the magnitude of thermodiffusion in the steady state. Although the above exponential distribution could motivate an approach based on Boltzmann equilibrium statistics, it is commonly argued that thermodiffusion without exception is a local nonequilibrium effect that requires fluid dynamics, force fields, or particle-solvent potentials (16)(17)(18)(19)(20). However, in a previous paper (15), we demonstrated that for moderate temperature gradients the thermal fluctuations of the particle are the basis for a local equilibrium.…”

Section: Theoretical Approachmentioning

confidence: 78%

“…In steady state, thermodiffusion is balanced by ordinary diffusion. Constant diffusion and thermodiffusion coefficients both lead to an exponential depletion law (15) Although the above exponential distribution could motivate an approach based on Boltzmann equilibrium statistics, it is commonly argued that thermodiffusion without exception is a local nonequilibrium effect that requires fluid dynamics, force fields, or particle-solvent potentials (16)(17)(18)(19)(20). However, in a previous paper (15), we demonstrated that for moderate temperature Fig.…”

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confidence: 88%

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Why molecules move along a temperature gradient

Duhr

Braun

2006

Proc. Natl. Acad. Sci. U.S.A.

902

987

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Molecules drift along temperature gradients, an effect called thermophoresis, the Soret effect, or thermodiffusion. In liquids, its theoretical foundation is the subject of a long-standing debate. By using an all-optical microfluidic fluorescence method, we present experimental results for DNA and polystyrene beads over a large range of particle sizes, salt concentrations, and temperatures. The data support a unifying theory based on solvation entropy. Stated in simple terms, the Soret coefficient is given by the negative solvation entropy, divided by kT. The theory predicts the thermodiffusion of polystyrene beads and DNA without any free parameters. We assume a local thermodynamic equilibrium of the solvent molecules around the molecule. This assumption is fulfilled for moderate temperature gradients below a fluctuation criterion. For both DNA and polystyrene beads, thermophoretic motion changes sign at lower temperatures. This thermophilicity toward lower temperatures is attributed to an increasing positive entropy of hydration, whereas the generally dominating thermophobicity is explained by the negative entropy of ionic shielding. The understanding of thermodiffusion sets the stage for detailed probing of solvation properties of colloids and biomolecules. For example, we successfully determine the effective charge of DNA and beads over a size range that is not accessible with electrophoresis.DNA ͉ fluorescence ͉ microfluidic ͉ Soret ͉ thermodiffusion T hermodiffusion has been known for a long time (1), but its theoretical explanation for molecules in liquids is still under debate. The search for a theoretical understanding is motivated by the fact that thermodiffusion in water might lead to powerful all-optical screening methods for biomolecules and colloids. Equally well, thermodiffusion handles and moves molecules alloptically and therefore can complement well established methods: for example, electrophoresis or optical tweezers. For the latter, forces of optical tweezers scale with particle volume and limit this method to particles of only Ͼ500 nm. Electrophoresis does not suffer from force limitations but is difficult to miniaturize because of electrochemical reactions at the electrodes.On the other hand, thermodiffusion allows the microscale manipulation of small particles and molecules. For example, 1,000-bp DNA can be patterned arbitrarily in bulk water (Fig. 1). The temperature pattern ''DNA,'' heated by 2 K, was written into a water film with an infrared laser scanning microscope. The concentration of 1,000-bp DNA was imaged by using a fluorescent DNA tag. In an overall cooled chamber at 3°C, DNA accumulates toward the heated letters ''DNA'' (negative Soret effect), whereas at room temperature DNA is thermophobic (positive Soret effect) as seen by the dark letters.In the past, the apparent complexity of thermodiffusion prevented a full theoretical description. As seen for DNA in Fig. 1, molecules characteristically deplete from regions with an increased temperature, but they can also show the inver...

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Section: Theoretical Approachcontrasting

confidence: 83%

Section: Theoretical Approachmentioning

confidence: 78%

mentioning

confidence: 88%

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Why molecules move along a temperature gradient

Duhr

Braun

2006

Proc. Natl. Acad. Sci. U.S.A.

902

987

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“…Thermophoresis has the potential to analyze the particle-solvent interaction of nanoscaled particles and biomolecules. Moreover, it is a versatile tool to manipulate or concentrate molecule concentrations in solution [12,13]. In addition to biotechnological applications, a natural thermophoretic setting is found in pores of rock near hot springs on the floor of the ocean, possibly involved in molecular evolution [14,15].…”

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confidence: 99%

Thermophoretic Depletion Follows Boltzmann Distribution

2006

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Thermophoresis, also termed thermal diffusion or the Soret effect, moves particles along temperature gradients. For particles in liquids, the effect lacks a theoretical explanation. We present experimental results at moderate thermal gradients: (i) Thermophoretic depletion of 200 nm polystyrene spheres in water follows an exponential distribution over 2 orders of magnitude in concentration; (ii) Soret coefficients scale linearly with the sphere's surface area. Based on the experiments, it is argued that local thermodynamic equilibrium is a good starting point to describe thermophoresis.

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“…The Soret effect is thus also referred to as the thermal diffusion effect. This effect was discovered independently by Ludig in Vienna in 1856 and by Soret in Geneva in 1879, and it has been studied mostly in oxide [1], electrolyte [2] and polymer [3] solutions.…”

Section: Introductionmentioning

confidence: 90%