In our earlier paper [

2], we posed the question whether the reaction from simple, anorganically formed molecules, such as hydrogen cyanide and formamide (FA), into the building blocks of RNA could be promoted by the same accumulation mechanism. Formamide has been discussed as an educt for the formation of prebiotic molecules for almost 50 years [

3,

4,

5,

6,

7,

8]. Saladino et al. synthesized all nucleobases from concentrated aqueous FA solutions [

5]. In our previous work, we measured the thermophoretic properties of FA in water as a function of temperature and concentration and used these data to conduct finite element calculations. We investigated how the distribution of FA in water develops as function of time in hydrothermal pores, which underlie a temperature gradient. In pores with sufficiently large aspect ratios, we found a very high FA concentration in the order of 85 wt %, which can be reached even with very small initial concentrations, as low as

${10}^{-7}$ wt %, if the time for accumulation is long enough. In a previous study, restricted to the dilute regime, Baaske et al. [

1] found an exponential rise of the accumulation as function of the aspect ratio of the pore. In their study, they used the approximation

$\omega (1-\omega )\approx \omega $. Using the full expression, we identified three regimes of the accumulation fold: a weak exponential growth at low aspect ratios, a sharp rise in the intermediate range, and finally, a saturation of the accumulation fold at large aspect ratios. Independent of the initial concentration, these three regimes could always be identified, if it was possible to reach the high aspect ratios. Due to numerical instabilities this was not always the case, if the diffusion was too fast or the Soret coefficient too low. The focus of this work is to expand on our previous paper by additional time-dependent simulations and a heuristic model that explains the strong dependence of the accumulation on pore geometry as well as its progression with time.

Thermophoresis, also known as thermodiffusion or Ludwig-Soret effect, is the mass diffusion of particles or molecules induced by a temperature gradient [

9]. Several theoretical approaches exist to describe thermodiffusion of polymer solutions, colloidal suspensions, and other liquid mixtures [

10,

11,

12,

13]. A good overview on the physics of the effect is given by the recent reviews by Würger [

11] and by Köhler and Morozov [

13], highlighting theoretical and experimental aspects of the phenomena for colloids and non-polar liquid mixtures, respectively. Further, simulations have been performed to investigate attractive and repulsive interactions between charged and uncharged colloidal particles [

14,

15] or to study the influence of chain length and stiffness of polymers [

16]. For aqueous low molecular weight mixtures, specific interactions and the addition of salt have been investigated [

17,

18]. The influence of interfacial effects on the thermophoresis have been studied systematically using microemulsions [

19], but it turned out that it was not possible to describe the experimental results by using existing theories [

19,

20]. The best agreement between experiment and theoretical concepts are found for charged spherical and rod-like colloids [

21,

22,

23], but when interfacial effects like the coverage by surfactants play a role, existing theoretical concepts fail [

24]. For polar liquid mixtures, such as aqueous FA solutions, there is so far no microscopic theory to describe thermophoresis. In a binary fluid mixture the mass flux in a temperature gradient can be expressed as

with contributions from the thermodiffusion along the temperature gradient

$\sim -{D}_{\mathrm{T}}\phantom{\rule{0.166667em}{0ex}}\overrightarrow{\nabla}T$ and from the Fickian diffusion along the resulting concentration gradient

$D\overrightarrow{\nabla}w$. For a stationary temperature gradient, the Fickian diffusions balances after some time the thermodiffusion and a steady state is reached. This defines the Soret coefficient

${S}_{\mathrm{T}}={D}_{\mathrm{T}}/D$, which is also a measure for the resulting concentration gradient, if a certain temperature gradient is applied. Generally, the magnitude of the Soret coefficient becomes larger, if the diffusion slows down. This implies that for slow diffusing molecules or particles smaller gradients are required to obtain the same concentration difference. Aqueous systems are of special interest due to their relevance in biotechnology. While charge contributions to the thermophoresis of solute molecules are well understood, the influence of contributions by the hydration layer are still unclear. It is known that the breaking of hydrogen bonds due to the surrounding solvent increases the Soret coefficient

${S}_{\mathrm{T}}$ of the solute molecules. To induce a breakage of hydrogen bonds, one can add an ingredient with a strong affinity to water [

25] or the bonds can be disrupted by increasing the temperature [

26]. This leads to a temperature dependence of

${S}_{\mathrm{T}}$ that is alike for a great number of biological and synthetic molecules in water [

27]. Iacopini and Piazza [

28] descibed the dependence with the empirical equation

where

${S}_{\mathrm{T}}^{\infty}$,

${T}^{*}$ and

${T}_{0}$ are fitting parameters. Recently, it became clear that the number of hydrogen-bond sites in the solute molecule is an important parameter when describing the temperature dependence of

${S}_{\mathrm{T}}$ and the thermodiffusion coefficient

${D}_{\mathrm{T}}$. It turns out that, for solutes belonging to a homologous series, there is a linear dependence of

${S}_{\mathrm{T}}$ to the difference of donor and acceptor sites [

29]. Although the reason for this linearity is not yet clear, it can be safely assumed that hydrogen bonding is relevant to the FA/water system as well.