M Bossert

A Grosman

I Trimaille

C Noûs

E Rolley

Stress or strain does not impact sorption in stiff mesoporous materials

The present paper investigates strain-induced sorption in mesoporous silicon. Contrarily to a previous report based on indirect evidence, we find that external mechanical strain or stress has no measurable impact on sorption isotherms, down to a relative accuracy of 10 -3 . This conclusion is in agreement with the analysis of sorption-induced strain of porous silicon, and holds for other stiff mesoporous materials such as porous silicas.

INTRODUCTION

The deformation of a porous material upon fluid adsorption has attracted much interest for a long time because of its importance in many situations such as drying of concrete, swelling of coal and shale. Recently, the adsorption-induced strain has been measured for various nanoporous or microporous materials (see recent reviews by Gor et al. [START_REF] Gor | Adsorption-induced deformation of nanoporous materials -A review[END_REF] and Vandamme [START_REF] Vandamme | Coupling between adsorption and mechanics (and vice versa)[END_REF]). At low vapor pressure, contraction or swelling may occur due to the competition between the attraction of adsorbed molecules to the pores walls and the packing effects; close to saturation pressure, swelling is usually observed. When the strains induced by adsorption are small, the calculation of the pressure in the fluid and the resulting strain of the solid skeleton can be uncoupled. In this limit, a thermodynamic approach based on the Derjaguin-Broekhoff-de Boer theory successfully accounts for the strain measured for instance in mesoporous silica [START_REF] Gor | Adsorption-induced deformation of mesoporous solids[END_REF], while non-linear density functional theory (NLDFT) is needed to describe the strain of microporous materials like zeolites [START_REF] Ravikovitch | Density functional theory model of adsorption deformation[END_REF]. Molecular dynamics is an alternative to NLDFT [START_REF] Schoen | Pore-lattice deformations in ordered mesoporous matrices: experimental studies and theoretical analysis[END_REF] and allows to take into account the coupling between the fluid adsorption and the porous network deformation [START_REF] Schoen | Phase transitions in nanoconfined fluids: Synergistic coupling between soft and hard matter[END_REF][START_REF] Puibasset | Adsorption-Induced Deformation of a Nanoporous Material: Influence of the Fluid-Adsorbent Interaction and Surface Freezing on the Pore-Load Modulus Measurement[END_REF]. The basic mechanisms responsible for adsorption-induced strain are now well understood in a variety of materials (see [START_REF] Gor | Adsorption-induced deformation of nanoporous materials -A review[END_REF] for further references).

As stressed by Vandamme [START_REF] Vandamme | Coupling between adsorption and mechanics (and vice versa)[END_REF], if adsorption deforms a solid, deformation should impact the sorption process, whatever the nature of the fluid, the pore size or the pore network geometry. This reverse process has only recently been investigated. For systems presenting a strong adsorption-induced deformation, the reverse process is easily observed in polymers [START_REF] Chen | Coupling of sorption and deformation in soft nanoporous polymers: Molecular simulation and poromechanics[END_REF], metal-organic framework [START_REF] Neimark | Stress-Based Model for the Breathing of Metal-Organic Frameworks[END_REF] and aerogels [START_REF] Herman | Deformation of silica aerogel during fluid adsorption[END_REF]. For coal, a much stiffer system for which the adsorption-induced strain is of order 10 -2 , the impact of an external stress on adsorption has also been quantitatively demonstrated [START_REF] Espinoza | Measurement and modeling of adsorptive-poromechanical properties of bituminous coal cores exposed to CO2: Adsorption, swelling strains, swelling stresses and impact on fracture permeability[END_REF].

Here, we are interested in still stiffer systems such as porous silica or porous silicon. For these materials, following the pioneering work of Amberg and McIntosh on disordered porous silica [START_REF] Amberg | A study of adsorption hysteresis by means of length changes of a rod of porous glass[END_REF], the interest in adsorption-induced strain has recently triggered many studies [START_REF] Grosman | Adsorption-induced strain of a nanoscale silicon honeycomb[END_REF][START_REF] Prass | Capillarity-driven deformation of ordered nanoporous silica[END_REF][START_REF] Balzer | Adsorption-Induced Deformation of Hierarchically Structured Mesoporous Silica-Effect of Pore-Level Anisotropy[END_REF][START_REF] Schappert | Unexpected Sorption-Induced Deformation of Nanoporous Glass: Evidence for Spatial Rearrangement of Adsorbed Argon[END_REF]. For such mesoporous materials, the maximal strain due to adsorption is of the order of 10 -3 , a small value which explains why the reverse impact of an external stress on fluid sorption is usually neglected. However, in a intriguing work, Grosman and Ortega [START_REF] Grosman | Influence of elastic strains on the adsorption process in porous materials: an experimental approach[END_REF] have observed that the sorption isotherms of nitrogen in porous silicon are shifted for porous samples still attached to the underlying silicon wafer with respect to free standing porous membranes. They explained that this shift was likely to be due to the stress in the supported sample, caused by the lattice mismatch between porous and bulk silicon [START_REF] Barla | Determination of lattice parameter and elastic properties of porous silicon by X-ray diffraction[END_REF]. They further argued [START_REF] Grosman | Influence of elastic deformation of porous materials in adsorptiondesorption process: A thermodynamic approach[END_REF] that the coupling between mechanics and adsorption could be responsible for inter-pore coupling. has triggered a renewed interest in the role of surface stress in the strain-adsorption coupling, pointed long ago by Eriksson [START_REF] Eriksson | Thermodynamics of surface phase systems: V. Contribution to the thermody-namics of the solid-gas interface[END_REF] (an illuminating discussion can be found in a recent article by Gor and Bernstein [START_REF] Gor | Revisiting Bangham's law of adsorption-induced deformation: changes of surface energy and surface stress[END_REF]). However, the relevance of surface stress in porous silicon is still controversial [START_REF] Puibasset | Adsorption-desorption hysteresis of simple fluids confined in realistic heterogeneous silica mesopores of micrometric length: A new analysis exploiting a multiscale Monte Carlo approach[END_REF][START_REF] Naumov | Understanding capillary condensation and hysteresis in porous silicon: Network effects within independent pores[END_REF], and more generally, the amplitude and the possible consequences of strain-induced adsorption in stiff mesoporous materials is still an open question.

In the present paper, we report on experiments designed specifically to settle this point. We have designed two different setups which allow to control either the strain or the stress of a single porous silicon sample. In both cases, we find that the change in the sorption isotherms is below the experimental resolution. We show that this conclusion is actually consistent with earlier measurements of adsorption-induced strain [START_REF] Grosman | Adsorption-induced strain of a nanoscale silicon honeycomb[END_REF][START_REF] Rolley | Using capillary forces to determine the elastic properties of mesoporous materials[END_REF]. The apparent discrepancy between the present experimental results and the observations by Grosman and Ortega could be due to the fact that they compare the sorption in different samples. The difference in fabrication processes between supported samples and free membranes could cause a small change in the structure of the porous layers, hence some changes in the sorption isotherms. Finally, we discuss the amplitude of stress-induced adsorption in other materials and show that these effects are negligible for stiff mesoporous materials such as porous silicas.

MATERIALS AND METHODS

Porous silicon samples. The preparation process, the morphology, and the physical properties of p+-type porous silicon have been reported elsewhere [START_REF] Grosman | Capillary condensation in porous materials. Hysteresis and interaction mechanism without pore blocking/percolation process[END_REF] so that we give here only a brief outline of these properties. In particular, the determination of pore size distribution from electron microscopy imaging is reported in detail in ref. [START_REF] Grosman | Capillary condensation in porous materials. Hysteresis and interaction mechanism without pore blocking/percolation process[END_REF]. Porous silicon is obtained by anodic dissolution of highly boron doped (100) Si single crystal in hydrofluoric acid solution. The pores are perpendicular to the wafer surface. The pore cross sections have a polygonal shape, with a broad pore size distribution, which depends on the etching conditions: for a nominal porosity of 50%, the transverse dimension of the pores is d = 13 nm, with 7 < d < 20 nm. For a nominal porosity of 70%, d = 26 nm, with 12 < d < 40 nm.

It has been shown [START_REF] Grosman | Capillary condensation in porous materials. Hysteresis and interaction mechanism without pore blocking/percolation process[END_REF], that the porosity is invariant along the pore axis and independent on the thickness of the porous layer. However, recent measurements of diffusion constants along and transverse to the the pore axis suggest that there are some connections between neighboring pores and also some constriction along the pores [START_REF] Puibasset | Structure and Permeability of Porous Silicon Investigated by Self-Diffusion NMR Measurements of Ethanol and Heptane[END_REF][START_REF] Kondrashova | Scale-dependent diffusion anisotropy in nanoporous silicon[END_REF].

At the end of the preparation process, once the desired thickness (i.e. pore length) is reached, the anodic current can be switched off to produce a supported porous layer attached to the Si substrate (Fig 1b). Alternatively, the current can be increased to dissolve the Si walls at the bottom of the pores. One thus obtains a free standing porous membrane (Fig 1a).

In this work, the thickness of the membranes is 20 or 50 µm, that of the supported layers ranges from 4 to 20 µm. We also used a third geometry, where the upper porous layer lies on an intermediate layer of higher porosity, and hence softer, attached to the silicon substrate (Fig. 1c). This duplex geometry is achieved by changing the etching parameters [START_REF] Grosman | Cavitation in Metastable Fluids Confined to Linear Mesopores[END_REF]. In this case, the mechanical coupling between the upper layer (the layer of interest) and the substrate is intermediate between a membrane and a supported layer, and this coupling can be tuned by changing the thickness (6 to 60 µm) of the intermediate layer. In all cases, we note and σ the components of the strain and stress tensor along the pore axis (fig. 1). Porous silicon is a transverse isotropic material [START_REF] Rolley | Using capillary forces to determine the elastic properties of mesoporous materials[END_REF]: when samples are submitted to a biaxial transverse stress, the transverse strain ⊥ and stress σ ⊥ are invariant through any rotation around the pore axis. Sorption isotherms. Sorption experiments are performed at T = 18 • C, the fluids used being n-hexane or n-heptane. Admission of fluid in the cell is controlled with a precision needle valve and the vapor pressure P is measured with a pressure transducer. The cell is equipped with an optical window for measuring either the deformation of the sample or the amount of adsorbed fluid. The later is determined through White Light Interferometry (WLI): when the porous layer is illuminated by a white light beam, the interference between the two beams reflected at both side of the porous layer creates oscillations in the spectrum of the reflected light. The analysis of these oscillations yields the optical thickness L of the layer [START_REF] Pacholski | Biosensing using porous silicon double-layer interferometers: reflective interferometric Fourier transform spectroscopy[END_REF][START_REF] Casanova | Gas adsorption and capillary condensation in nanoporous alumina films[END_REF]. In contrast with standard volumetric techniques which require integration of the fluid flow in the cell, L measurement is instantaneous, and the variation of the thickness due to adsorption can be tracked at the acquisition rate of the spectrometer (about 0.1 Hz), so that the optical sorption isotherms L vs P appear as continuous curves (see Supplementory

Information for details about the setup and the spectrum analysis).

The raw output of WLI is L = 2n ef f l , where l is the geometrical thickness of the porous layer along the pore axis, which may change slightly along an isotherm, and the effective optical index n ef f which depends on the adsorbed amount (mole number N ) in the pores. So the change ∆L = L(P ) -L(0) reflects the change in N . Sorption isotherms will be displayed as ∆L(P ), or as the normalized change ∆L/∆L M = ∆L/(L(P sat ) -L(0)) in order to compare samples with different thicknesses (P sat is the saturated vapor pressure). The resolution is limited by small heterogeneities of the samples: changing the mechanical control parameters causes a small displacement of the sample with respect to the illuminating light beam. The relative reproducibility is about 10 -3 .

Calculating N from ∆L requires first to choose an effective medium model among many [START_REF] Markel | Introduction to the Maxwell Garnettapproximation: tutorial[END_REF] and, second, a precise knowledge of many parameters such as the porosity, the optical index of the liquid..., which may change along the isotherm. Here, we have chosen to measure L vs N directly for a porous silicon sample (see Appendix). We find that ∆L is proportional to N within a few percent. It means that the shape of an optical isotherm ∆L(P ) is very similar to a true sorption isotherm N (P ). More importantly here, the impact of an external mechanical parameter, for instance ⊥ , measured by [N (P, ⊥ ) -N (P, 0)] /N (P sat , 0), is equal within a few percent to the normalized change of the optical thickness [∆L(P, ⊥ ) -∆L(P, 0)] /∆L M and the final resolution is still 10 -3 . This is enough for observing the same effect as Grosman and Ortega, which is of the order of a few percent [START_REF] Grosman | Influence of elastic strains on the adsorption process in porous materials: an experimental approach[END_REF].

Controlling strain. The strain of the sample is easily controlled when using supported layers. The compliance of the layer is much smaller than that of the underlying substrate, so that the strain of the sample is fixed by the strain of the wafer itself. By bending the wafer to a spherical cap, we could reach biaxial strain ⊥ up to approximately 10 -3 .

Controlling stress. In this case, we use 50% porosity membrane of thickness 50 µm.

The transverse dimensions are 10×15 mm 2 . One short side is glued to a fixed frame and the opposite side is glued to a piezo ceramic bimorph. The stiffness of the bimorph is much smaller than that of the membrane, so that the voltage on the piezo controls the force F directed along the long side of the membrane, hence the stress σ ⊥ of the membrane. The bimorph response was calibrated prior to the experiment: the stress can reach about 10 MPa.

During the sorption experiment, we measure the strain ⊥ along F. In this experiment, the aspect ratio is too close to one for the strain to be really unixial, but this will not prevent us from drawing a qualitative conclusion.

RESULTS

Supported layer submitted to controlled strain. We have first investigated the impact of a biaxial strain on sorption isotherms. The result is shown in fig. 2 for a layer of 70% porosity, 20 µm thick, and for n-hexane. The blue isotherm corresponds to a supported layer as prepared. Note that because of the lattice mismatch between bulk and porous silicon [START_REF] Barla | Determination of lattice parameter and elastic properties of porous silicon by X-ray diffraction[END_REF], the residual strain in this reference state is not strictly zero. The red isotherm is measured after changing the biaxal strain by ⊥ = 8.3 × 10 -4 . The two curves are almost perfectly superimposed, the upper bound for |∆L(P, ⊥ ) -∆L(P, 0)|/∆L M is 2 × 10 -3 . The change in the position of the hysteresis loop is at most 2 × 10 -3 P sat . These changes are of the order of the reproducibility of the experiment, and one order of magnitude smaller than the effect reported by Grosman and Ortega.

Membrane submitted to controlled stress. In a second step, we have investigated the change in adsorbed amount when a porous sample is submitted to an external stress σ ⊥ , approximately uniaxial. In this experiment, we monitor the average strain ⊥ as a function of the vapor pressure P for different values of σ ⊥ . Strain isotherms are shown in figure 3, for heptane and a 50% porosity membrane. The shape of these isotherms reflects the changes in capillary forces along a sorption isotherm and have been discussed in a previous paper [START_REF] Grosman | Adsorption-induced strain of a nanoscale silicon honeycomb[END_REF]. The only effect of applying an external stress σ ⊥ = 7 MPa is to translate the isotherm as a whole. In particular, we find again that the shift in pressure of the hysteresis loop, if any, is smaller than 2 × 10 -3 P sat .

As deformations are of the order of a few micrometers, strain measurements are extremely sensitive to a small drift of the relative position of the camera and the experimental cell. This explains why the two strain isotherms do not superimpose as exactly as sorption isotherms in figure 2. In order to look for even a tiny effect of stress on adsorption, we fix the vapor pressure and monitor the amount of adsorbed fluid with WLI when applying an external stress of 7 MPa. As for the strain-controlled experiment, the change in |∆L(P, σ ⊥ )-∆L(P, 0)|/∆L M is smaller than the resolution.

DISCUSSION

The experimental results are quite clear: adsorption is not modified when a mechanical control parameter is changed. Before going back to the experiments by Grosman and Ortega, who claimed to observe stress-induced adsorption, it is necessary to check whether the present result is consistent with data on adsorption-induced stress or strain, which has been measured in detail for heptane in poSi. [START_REF] Grosman | Adsorption-induced strain of a nanoscale silicon honeycomb[END_REF][START_REF] Rolley | Using capillary forces to determine the elastic properties of mesoporous materials[END_REF].

Back to thermodynamics

As we are not interested here in the details of adsorption at the pore scale, we follow the simple thermodynamic approach by Brochard et al. [START_REF] Brochard | Poromechanics of microporous media[END_REF]. The system we consider is the elastic porous matrix and the fluid inside the pores, in isothermal condition.

When the stress σ ⊥ transverse to the pore axis is biaxial, the strain ⊥ is the same in any directions perpendicular to the pore direction. Let f be the Helmhotz free energy per unit of undeformed volume. Its differential may be written:

df = σ d + 2σ ⊥ d ⊥ + µdn ( 1
)
where µ is the chemical potential of the fluid and n is the number of moles of fluid N divided by the volume V 0 of the sample in its reference (undeformed) state. If the stress is uniaxial, perpendicular to the pore axis, df is unchanged except for the factor 2 which disappears in the second term.

Then the Maxwell relations associated with (f -µn) yield for instance the variation of the amount of fluid n as a function of the biaxial strain ⊥ :

∂n ∂ ⊥ ,µ = -2 ∂σ ⊥ ∂µ , ⊥ (2)
Assuming that the gas is perfect, µ(P ) -µ(P sat ) = R T ln(P/P sat ). It is more convenient to express µ in term of the pressure P L ≡ P sat + µ/v L , where v L is the liquid molar volume at coexistence. If the liquid is incompressible and for large enough pores, P L is simply to the liquid pressure in the pores, or the Laplace pressure. Then Eq. 2 may be written:

∂N ∂ ⊥ ,µ = - 2V 0 v L ∂σ ⊥ ∂P L , ⊥ (3)
The quantity that can be derived from the experiment is (N (P, ⊥ ) -N (P, 0))/N M where N M = N (P sat , 0). Neglecting the change of volume between the empty sample and the sample at saturation and assuming that the liquid in the pore has the bulk liquid density,

N M = φ 0 V 0 /v L
where φ 0 is the porosity in the reference state. Thus we obtain:

N (P, ⊥ ) -N (P, 0) N M = - 2 φ 0 ∂σ ⊥ ∂P L , ⊥ ⊥ (4)
In the same way, one can compute the change in N when the sample is submitted to a uniaxial stress σ ⊥ :

N (P, σ ⊥ ) -N (P, 0) N M = 1 φ 0 ∂ ⊥ ∂P L ,σ ⊥ σ ⊥ (5)
The quantities appearing on the right-hand-side of equations 4 and 5 can be obtained by measuring the mechanical response of a sample along a sorption isotherm. For instance, for a supported porous layer, the biaxial stress in the layer can be calculated from the curvature of the wafer (see ref. [START_REF] Grosman | Adsorption-induced strain of a nanoscale silicon honeycomb[END_REF][START_REF] Rolley | Using capillary forces to determine the elastic properties of mesoporous materials[END_REF] for details). Two such stress isotherms σ ⊥ vs P are shown for heptane in figure 4. Computing the response coefficient makes sense only for the reversible regions, below or above the hysteresis loop. In the low pressure regime (P < 0.05 P sat ), one finds ∂σ ⊥ /∂P L | , ⊥ is about 7 × 10 -3 and 3 × 10 -3 for 50% and 70% porosity sample, respectively. In the saturation regime, ∂σ ⊥ /∂P L | , ⊥ -0.2 and -0.4 for 50% and 70% porosity respectively. These coefficients do not depend on the nature of the fluid [START_REF] Rolley | Using capillary forces to determine the elastic properties of mesoporous materials[END_REF], so that they can be used either for heptane or hexane. The stress-induced sorption has the opposite sign in the two reversible regions. That reflects the fact that, upon adsorption in a free sample, contraction is observed at low pressure, while expansion is observed when the sample is saturated [START_REF] Grosman | Adsorption-induced strain of a nanoscale silicon honeycomb[END_REF]. Using theses values of the response coefficients and eq. 4, it is straightforward to estimate the impact of a variation of the external strain on the isotherm. In the most favorable case (70% porosity, saturated sample), (N (P, ⊥ ) -N (P, 0))/N M ∼ ⊥ : the amount of fluid at saturation should increase very slightly when the porous layer is stretched, but the magnitude of the effect is comparable to the resolution, even for the highest strain we can achieve. In the reversible low pressure region of the isotherms, the shift in N is roughly two order of magnitude smaller. One finds the same orders of magnitude for stress-induced sorption.

In conclusion, thermodynamics predicts that strain-induced or stress-induced adsorption in porous silicon is too small to be observed, in perfect agreement with the experiments.

Membranes vs supported layers

So far, our experiments show that mechanics cannot explain the observation by Grosman and Ortega that adsorption isotherms for a 20 µm thick membrane is shifted compared to a supported layer having the same thickness and same porosity (50%). As this shift was observed only for nitrogen at 77 K, we first checked that it is still present for hexane (fig. 5a). We find that the shift in pressure is about 5% of P sat , similar to that of nitrogen.

We have also used a different strategy in order to vary the coupling between the porous layer and the wafer progressively: a sublayer with a larger porosiy is etched below the 50% porosity layer of interest (fig. 1c) whose pores are opened at both ends for all the samples. As shown in figure 5b, when the sublayer thickness increases, the hysteresis loop shifts towards higher pressure and there is a small decrease in the adsorbed amount at low pressure. supported layers with sublayers between the layer of interest and bulk silicon (fig. 1c).

When increasing the sublayer thickness, the variation of the stress in the upper layer is smaller than in the direct experiments described in the previous section, so that a direct mechanical effect can again be ruled out. In this series, the ends of the pores are similar for all the samples so that boundary conditions cannot explain the shift in figure 5b either.

The only explanation is that the structure of the upper layer changes as the sublayer grows.

The sublayer being etched at constant speed, the upper layer under study is submitted to the electro-etching conditions for a time which increases with the sublayer thickness (in the same way, compared to supported samples, membranes are submitted to a strong current density when they are detached from the substrate). A simple interpretation of the shift of the isotherms would be that the mean transverse dimension of pores increases slightly as a function on time, due to a small residual dissolution. Using a very crude Kelvin model, for a total etching time of about 1 hour, the 5% shift of the emptying pressure requires a 10% increase of the mean pore diameter. This is not consistent with the fact that the porosity of poSi layers is found to be independent of the thickness [START_REF] Grosman | Capillary condensation in porous materials. Hysteresis and interaction mechanism without pore blocking/percolation process[END_REF]. So we rather suspect that the shift is due to a subtle change in the shape of the pore, residual dissolution occurring mainly at some defects at the inner surface of the pores, thus leading to a decrease in the effective diameter of the pore without changing much the porosity. This hypothesis could be checked by high resolution transmission electronic microscopy.

Comparison with other porous materials

The coefficient ∂ ⊥ /∂P L appearing in eq. 5 is simply the inverse of the pore load modulus M ⊥ , which has been measured for many materials. As we are interested here in order of magnitude, let us assume that the material is isotropic, characterized by a single pore modulus M and a bulk modulus K. In this limit, for a sample submitted to an isotropic stress σ eq. 5 reads: N (P, σ) -N (P, 0)

N M = 1 φ 0 K M v ( 6
)
where v is the volumetric strain.

In the context of isotropic microporous materials, the coupling between the volumetric strain v and adsorption is rather quantified by a coupling parameter C defined by [START_REF] Brochard | Poromechanics of microporous media[END_REF]:

n(µ, ) -n(µ, 0) n(µ, 0) = C(µ) v (7)
So the importance of strain-induced sorption (or mechanosorptive effect) depends on the coupling parameter C (or on the quantity K/(φ 0 M )) and on the maximum strain v,M that can be achieved.

For a polymeric material, such as cellulose network, C ∼ 10 [8] and v,M ∼ 0.1 , so that the relative change of n is of order 1: the mechanosorptive effect is very large in this type of material. For aerogels, φ 0 ∼ 1 and K ∼ M [START_REF] Herman | Deformation of silica aerogel during fluid adsorption[END_REF], so that C ∼ 1. As aerogels can withstand large strains, stress-induced sorption is still important.

Let us now consider less compliant materials, where the mechanosorptive effect is expected to be smaller. For microporous carbon it is found that C ∼ 10 and v,M ∼ 0.01 for methane [START_REF] Brochard | Poromechanics of microporous media[END_REF] or CO 2 adsorption [START_REF] Espinoza | Measurement and modeling of adsorptive-poromechanical properties of bituminous coal cores exposed to CO2: Adsorption, swelling strains, swelling stresses and impact on fracture permeability[END_REF] resulting in a small but measurable coupling.

Data is also available for several type of porous silicas. For microporous silicas, such as faujasite zeolite [START_REF] Ravikovitch | Density functional theory model of adsorption deformation[END_REF], M is close to K, resulting in C of order 1. This holds also for ordered mesoporous silicas, such as SBA16, MCM41s [START_REF] Prass | Capillarity-driven deformation of ordered nanoporous silica[END_REF], and for Vycor, a disordered system (see ref. [START_REF] Amberg | A study of adsorption hysteresis by means of length changes of a rod of porous glass[END_REF][START_REF] Vichit-Vadakan | Measuring Permeability of Rigid Materials by a Beam-Bending Method: II, Porous Glass[END_REF] for numerical value of the elastic parameters). For all this materials, the coupling parameter is thus close to the one of porous silicon (C = 0.3). As the maximum strain is in the range 10 -4 -10 -3 , it turns out that, for all this systems, the relative change in the adsorbed amount is 1% at most, below the resolution of standard volumetric and gravimetric techniques.

CONCLUSION

We have designed experiments to measure sorption isotherms of porous silicon, with samples submitted to an external stress or strain. We could not detect any change in the isotherms, in agreement with earlier measurements of sorption-induced strain. It is likely that strain-induced sorption is also negligible for most microporous or mesoporous silicas.

As a consequence, we can rule out the proposal by Grosman and Ortega that mechanics is responsible for the difference between isotherms of supported (stressed) or free standing (relaxed) samples of porous silicon. This difference could be due to small changes in the geometry of the pores during the etching process; testing this hypothesis requires a better characterisation of the pore network.

FIG. 1 .

 1 FIG. 1. Geometry of the samples: free membrane (a), supported layer (b) and duplex layer (c). In the later case, the porous layer of interest is the upper one.

FIG. 2 .

 2 FIG. 2. Optical sorption isotherms for a 70% porosity sample under imposed bixial strain (fluid: hexane). The change ∆L of the optical thickness is plotted as function of the reduced vapor pressure. Changing the transverse strain by 8 × 10 -4 has no measurable impact on the isotherm.

FIG. 3 .

 3 FIG. 3. Strain isotherms for a 50% porosity membrane (fluid: heptane). The strain ⊥ is measured along the direction of the applied stress σ ⊥ and is plotted as function of the reduced vapor pressure. A first isotherm (blue line) is recorded at zero stress. After the actuation of the piezo bimorph (thick black arrow), a second isotherm (red line) is recorded for σ ⊥ = 7 MPa. Translating the second isotherm by -3.9 × 10 -4 yields the red dashed line: the hysteresis loop occurs at exactly the same pressure for σ ⊥ = 0 and σ ⊥ = 7 MPa.

FIG. 4 .

 4 FIG. 4. Transverse bixial stress as a function of normalized vapor pressure (fluid: heptane). Blue: 50% porosity, Red: 70% porosity. The absolute value of ∂σ ⊥ /∂P L | , ⊥ is maximum in the mbar region and when the sample is saturated.

FIG. 6 .

 6 FIG. 6. Optical thickness as a function of adsorbed amount for N 2 at 77.4 K. Diamonds: experimental data, dashed line: linear fit.

  Table Of Content Use Only

ACKNOWLEDGEMENTS

This paper is dedicated to the memory of our late co-author and colleague A. Grosman.

We thank P. Spathis, P.-E. Wolf and J. Puibasset for stimulating discussions and we are indebted to M. Vandamme for clarifying the connection between our measurements and poromechanics. We acknowledge the financial support of Agence Nationale de la Recherche through the project CavConf, ANR-17-CE30-0002, including the funding of M. B.

Converting the optical thickness L to the amount of fluid N . The output of interferometric measurement is the optical thickness L = 2n ef f l . When using this technique for studying adsorption in porous silicon [START_REF] Pacholski | Biosensing using porous silicon double-layer interferometers: reflective interferometric Fourier transform spectroscopy[END_REF][START_REF] Casanova | Controlling the role of nanopore morphology in capillary condensation[END_REF] or porous alumina [START_REF] Casanova | Gas adsorption and capillary condensation in nanoporous alumina films[END_REF], it is usually assumed that the geometrical thickness l does not change upon adsorption. For porous silicon, this is true within a relative accuracy of 10 -3 [START_REF] Rolley | Using capillary forces to determine the elastic properties of mesoporous materials[END_REF]. Then, n ef f is converted to the fraction g of the pore volume which is occupied by the liquid using a model for the effective medium consisting in 3 phases: silicon, liquid and vapor. This conversion requires first to chose a model among existing ones (Maxwell Garnet, various Bruggeman models... [START_REF] Markel | Introduction to the Maxwell Garnettapproximation: tutorial[END_REF]) and second to know precisely the optical indices of the silicon n Si and of the liquid n L , as well as the porosity φ. Again, the variation of φ is small along an isotherm, but that of n L is not negligible: actually, the change in the optical index of the liquid with P L is responsible for the slope of the saturation plateau in figure 5. In any case, most models predict a nearly linear dependence in g of the effective optical index n ef f . Hence, the optical thickness L should also vary roughly linearly with the amount of fluid N in the pores.

Given the difficulties of the conversion, we have decided to check the relation between L and N . To this end, we have measured L and N independently as a function of the vapor pressure P along a sorption isotherm. The sample was a 50% porosity supported layer, 20 µm thick. The volumetric isotherm N (P ) was measured using a commercial apparatus (HPVA II Micromeritics) equipped with a 1000 Torr pressure transducer. The fluid was nitrogen (instead of hexane to avoid any contamination of the apparatus) and the sorption isotherm was measured at 77.4 K. For measuring the optical isotherm L(P ) at the same temperature, we built an optical cell that can be attached to a nitrogen dewar (raw isotherms N (P ) and L(P ) are shown in the Supplementory Information).

As shown in figure 6, the optical thickness L varies linearly in the amount N of adsorbed fluid, within 5 %. So, changing a mechanical parameter causes the same relative shift of N and L, within 5 %.


Marianne Gaborieau
email: m.gaborieau@uws.edu.au

Sandy P S Koo

Patrice Castignolles

Tanja Junkers
email: thomas.junkers@uhasselt.be.

Christopher Barner-Kowollik
email: christopher.barner-kowollik@kit.edu.

Reducing the Degree of Branching in Polyacrylates via Midchain Radical Patching: A Quantitative Melt-State NMR Study

Keywords: acrylates, branching, solid-state NMR, melt-state NMR, kinetics (polym)

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Introduction

The radical polymerization of acrylates leads to polymers with a high degree of branching caused by the formation of so-called mid-chain radicals (MCRs). 1 Such mid-chain radicals are formed via intra-and inter-molecular (chain) transfer to polymer reactions caused by the high reactivity of the propagating radical species (secondary propagating radicals (SPR)). The generated MCRs (which can represent up to 80% of the total radical population at temperatures exceeding 80 C) 2, 3 can subsequently react with monomer units (albeit at a reduced rate compared to SPRs), 4 participate in bimolecular termination events (either with themselves or with SPRs) or undergo -scission reactions to yield macromonomer species and SPRs 5 (see Scheme 1). Scheme 1. Reaction pathways of mid-chain radicals (MCRs). In the presence of a chain transfer agent (CTA), the MCRs are transformed ("patched") into thiol-capped linear polyacrylate species (TCP). T is the initiating moiety arising from the initiator or the thiol.

Soft ionization mass spectrometry techniques allowed a detailed study of the product spectra that emerge from the radical polymerization of n-butyl acrylate (BA) in the presence of 1-octanethiol as a chain transfer agent (CTA). 6,7 The presence of the CTA -beside leading to a reduction in the molecular weight of the generated polymeric materials -greatly influences the product distribution of the obtained polymer. Specifically, with increasing concentrations of CTA, the amount of unsaturated -scission product was progressively reduced to levels where practically no -scission product was detected at intermediate temperatures and only low levels at elevated temperatures (note that under such conditions the majority of material usually consists of -scission products, quantitative data on what fraction of chains contain either the thiol-specific moiety or other endgroups have been provided before). [8][9][10][11] The explanation for such an observation can be provided by a rapid transfer of a hydrogen from the transfer agent to the relatively long-lived MCR at a higher rate than the MCR can undergo -scission (see Scheme 1). The hypothesis was also tendered that the degree of branching in the generated polymeric material would be significantly reduced by a similar amount as the formation of the -scission product is suppressed. 7 However, branching is not observable via electrospray ionization mass spectrometry (ESI-MS) due to the isobaric nature of the branched and linear structures. The only method for directly accessing the degree of branching in polyacrylates is quantitative 13 C NMR spectroscopy. 12 Quantitative 13 C NMR spectroscopy is no routine method. There have been several attempts to quantify the degree of branching in polyacrylates synthesized in various conditions, with various NMR methods. [12][13][14] Both resolution and sensitivity are required for a reliable quantification of the degree of branching. Initial attempts were carried out either on polymer solutions 13 or on swollen samples 14 ; they exhibit high resolution (owing to high sample mobility) but suffer from limited sensitivity (and thus low precision) partly due to limited sample concentration. Moreover, polyacrylates often exhibit a significant gel fraction and only the soluble fraction (and thus a fraction that assumingly consists of polymer with less branches) of the sample is measured in some cases. 12 Recently, however, a method has been proposed and validated to estimate the precision of the determined degree of branching from the signal-to-noise ratio of the quaternary carbon at the branching point. 12,15 As for any experimentally determined quantity, taking the precision into account allows for a meaningful comparison of samples. In an earlier study of the possible patching of MCRs, 7 an attempt was made to determine the degree of branching via 13 C NMR in solution. Unfortunately, the low signal-to-noise ratio of the quaternary carbon (5.5) led to a rather limited precision on the measured degree of branching (27 % according to Equation 2 below). A degree of branching in the range of 1.0 to 1.8 % of the monomer units at 140 C at a 1-octanethiol concentration of 0.4 mol•L -1 was found. No literature data allowed for direct comparison in terms of effect of CTA, and the somewhat higher value of close to 2 % found in some known systems with similarity (bulk) but at a far lower temperature (70 C) 16 was not significantly different. A general increase of the degree of branching with reaction temperature is expected, thus the similar results led to the speculation that the CTA lead to lower number of branches in the polymer. The latter measurement was obtained by fast-pulsing NMR. The latter measurement was obtained by fast-pulsing NMR, 13,16 yielding a precise but inaccurate value; a calibration carried out with a longer measurement time was not shown, 16 from which the precision could have been estimated. Therefore, although previous mass spectrometry results hinted at a MCR patcher (and thus branching suppression) effect, previous NMR results were not precise and accurate enough to confirm the effect.

We recently developed a reliable melt-state 13 C NMR method for the quantification of the degree of branching in polyacrylates. 12 Quantitative 13 C melt-state NMR is described in detail in the literature 12,15 and has also been used to quantify branching or chain ends in polyolefins. 15,[17][18][19] Melt-state NMR (using solid-state NMR equipment) is more sensitive than solution-or gel-based methods as it measures the pure (undiluted) sample. It yields sufficient resolution for branching quantification through the high mobility of polymer chains in the melt combined with magic-angle spinning and dipolar decoupling.

The accuracy of measured degrees of branching is ensured by full relaxation of the relevant signals between pulses. 12 In the current communication we employ the melt-state 13 C NMR method to compare degrees of branching in polyBAs synthesized with and without CTA (at various temperatures) and investigate whether the inclusion of an efficient hydrogen donor in the polymerization actually leads to a strong reduction in the degrees of branching observed in polyacrylates in agreement with the hypothesis tendered from earlier mass spectrometry results on the same system.

Experimental Section

Materials and radical polymerization in bulk at various temperatures, with or without 1octanethiol, were similar to those of previous works 6,7 . Long-chain branches can lead to a high level of brand broadening in size-exclusion chromatography (SEC). 20 The molecular weights from SEC might thus be of limited accuracy. 21 . The glass transition temperature (Tg) and decomposition temperature were measured for all samples using differential scanning calorimetry and thermogravimetric analysis. Details of materials, polymerization, SEC and thermal analysis can be found in the supporting information section.

Quantitative 13 C melt-state NMR experiments followed variations of a published method, 12 with single-pulse excitation under magic-angle spinning (SPE-MAS) at exactly Tg+150 °C (77 to 104 °C, more than 200 °C below their decomposition temperature) and 75.47 MHz with 10 s relaxation delay.

Nitrogen gas was used for all pneumatics. Samples synthesized with thiol were measured in 7 mm rotors at MAS rotational frequencies of 1.8 to 4.5 kHz, while samples synthesized without thiol were measured in 4 mm rotors at 9 kHz MAS (due to extensive crosslinking preventing their spinning in 7 mm rotors).Nitrogen gas was used for all pneumatics. More experimental NMR details are given in Supporting Information. The degree of branching (DB) was quantified in percents of the monomer units from the integrals I of the signals of the quaternary carbons (Cq) at 49 ppm and of the OCH2 moiety at 63 ppm, following Equation 1:

( ) ( ) 2 100 (%) OCH I C I DB q  = (1)
Note that due to a signal from 1-octanethiol overlapping with the backbone signal of polyBA, the latter could not be used for quantification. The full chemical shift assignment, known from literature, 14,22 is detailed in the Supporting Information section. The relative standard deviation SD of DB was calculated from the signal-to-noise ratio of the quaternary carbon SNR using Equation 2, established experimentally from branching measurements in polyethylene by 13 C melt-state NMR: 15

28 . 1 238 (%) SNR SD = (2)
Its deviation from the theoretically expected dependency of SD on 1/SNR (with only limited practical differences), and its wider applicability were discussed for branching measurements for poly(n-alkyl acrylates). 12

Results and Discussion

The presence of 1-octanethiol during the polymerization has significant effects on its mechanism and on the obtained polymer, such as a significant reduction in terminal double bonds, 7 as well as a decrease in molecular weight as demonstrated by calorimetry and SEC (see Tables S3 andS1 in Supporting Information). As the chain length of the polymer is expected to influence the local chain dynamics, which may change the conditions for recording quantitative 13 C melt-state NMR spectra, all spectra were recorded at exactly 150 °C above the Tg. The 13 C melt-state NMR spectra of the samples exhibiting the lowest and the highest DB are shown in Figure 1. The DB values measured for all samples are shown in Figure 2 with their precision, and listed in Table S3 (Supporting Information).

The degrees of branching obtained in the CTA-containing systems are significantly lower than the ones obtained in the conventional system for all temperatures as can be seen in Figure 2. The "patching" effect of tertiary mid-chain radicals by the CTA can thus be confirmed as operational. In addition, the degree of branching significantly increases with increasing temperature, for both the CTA and non-CTA systems. Such an observation is explicable by the increased frequency of the reactions that lead to the formation of MCRs, i.e. inter-molecular chain transfer as well as random intra-molecular transfer and backbiting. Typical activation energies for the rate coefficients governing these reactions may be 20

to 25 kJ mol -1 higher than that of propagation. 1 At the same time, the transfer rate of the CTA onto the MCR may be hypothesized to be similar to the one of propagation. Therefore -even though the CTA is capable of reducing the amount of branching significantly -its effectiveness decreases with increasing temperature. Generally, it should be noted that of course the CTA not only reduces the amount of branching, but also the average chain length of polymers. The reduction of chain length is however a separate effect that may influence the number of branches per chain (as expected in pulsed laser polymerization), 4,23 but does not directly influence the number of branches per monomer unit (degree of branching). The conventional transfer to the CTA does not change the (macro-)radical concentration, hence the frequency at which transfer to polymer reactions occur is unchanged. As MCRs, once they are formed are then either "patched" (which in fact is a conventional transfer to CTA reactions itself), undergo scission or form a chain branch, the number of branches per chain units or the concentration of scission products is not affected by the chain-length reducing action of the CTA. Overall the NMR results confirm and support our previous mass spectrometric findings relating to the -scission products 6,7 as the reduction in degree of branching and the reduction in the amount of -scission product correspond well with each other. The degrees of branching obtained in this work moreover now allow for more detailed investigations into the kinetics of acrylate polymerizations. Both mass spectrometric and NMR spectroscopic data are highly complementary to each other. Together they provide a complete microstructural image of the obtained polymer product. Even though numerous studies have shown by 13 C NMR that branching plays an important role, only with the present work reliable quantitative data have been come available for a systematic variation of reaction conditions that can be utilized for further kinetic and mechanistic studies that will help to find improved conditions in polyacrylate synthesis in numerous applications.

Conclusions

Degrees of branching were measured with 13 C melt-state NMR in poly(n-butyl acrylates) synthesized in both the presence and absence of 1-octanethiol at various temperatures, and their precision calculated based on the signal-to-noise ratio of the quaternary carbon at the branching point. A significant decrease of branching was observed in the presence of a thiol during the polymerization process, experimentally confirming the "patching" effect of mid-chain tertiary radicals by the thiol.

Thus, the addition of a chain transfer agent not only controls the chain length of the polyacrylate, but also the complexity of its microstructure is significantly reduced. The current work illustrates the potential of melt-state NMR for the quantitative determination of the degrees of branching, with precision, for example for kinetics studies 24 .

Acknowledgements

Figure 1 .

 1 Figure 1. Melt-state 13 C SPE-MAS NMR spectra recorded at Tg+150 °C for poly(n-butyl acrylate)

Figure 2 .

 2 Figure 2. Degree of branching (in percent of monomers units) as a function of the reaction

  . C.B.-K. acknowledges funding from the Karlsruhe Institute of Technology (KIT) in the context of the Excellence Initiative for leading German universities, the German Research Council (DFG) as well as the Ministry of Science and Arts of the state of Baden-Württemberg. T.J. is grateful for support from the Fonds der Chemischen Industrie. M.G. thanks Dr Robert Graf (MPIP) for fruitful discussions and Prof H.W. Spiess (MPIP) for support. Supporting Information Available: Experimental details and results for polymerization, sizeexclusion chromatography, thermal analysis and 13 C NMR. This material is available free of charge via the Internet at http://pubs.acs.org. for Table of Contents use only for Reducing the Degree of Branching in Polyacrylates via Mid-Chain Radical Patching: A Quantitative Melt-State NMR Study by Marianne Gaborieau, Sandy P.S. Koo, Patrice Castignolles, Thomas Junkers, and Christopher Barner-Kowollik

Supporting

Polymerization

Materials n-Butyl acrylate (BA, Fluka, 99%) monomer was de-inhibited over a column of activated basic alumina. 2,2-azoisobutyronitrile (AIBN, DuPont) was recrystallized twice from methanol before use. 1octanethiol (Aldrich, 98.5%) was used as received. Please note that n-butyl acrylate is toxic, irritant, and can induce sensitization.

Polymerization

All samples were prepared as follows: each sample consisted of BA (sample volume ~3.0 mL) with an initiator concentration (AIBN) of 5•10 -3 mol•L -1 and 1-octanethiol concentration of 0 or 0.4 mol•L -1 . BA, initiator (and thiol) were placed in a Schlenk flask, and purged of gas via the freeze-pump-thaw method. Upon complete degassing, the samples were kept under a nitrogen atmosphere. Samples were heated at the reaction temperature for 8 h, 40 min and 20 min respectively for temperatures of 60 °C, 100 °C or 140 °C with stirring, after which time the samples were quenched in ice water. Excess unreacted thiol compound and residual monomer were removed under vacuum on a Schlenk line at ambient temperature for 5 days, with periodic stirring to help release residual monomer and thiol. The polymerization times were calculated by doubling the time estimated from the first order kinetic decomposition equation to result in full dissociation of initiator into radicals, i.e, until > 99 % of initiator is decomposed. Monomer conversion was determined to be > 95 % for all samples by gravimetry.

Size-Exclusion Chromatography

Experimental conditions. SEC measurements were performed on a Polymer Laboratories PL-GPC 50 Plus Integrated System, comprising an autosampler, a PLgel 5µm bead-size guard column (50 x 7.5 mm) followed by one PLgel 5μm Mixed E column (300 x 7.5 mm), three PLgel 5µm Mixed C columns (300 x 7.5 mm) and a differential refractive index detector using THF as the eluent at 35 °C with a flow rate of 1 mL•min -1 .

The SEC system was calibrated using linear polystyrene standards ranging from 160 to 6•10 6 g•mol -1 and linear poly(methyl methacrylate) standards ranging from 700 to 2•10 6 g•mol -1 . The molecular weights were calculated using the universal calibration principle and the Mark-Houwink-Sakurada of polystyrene, 1 poly(methyl methacrylate) 1 and poly(n-butyl acrylate) 2 .

It should be noted that the presence of long-chain branching may lead to incomplete separation in SEC. It may introduce an error up to 100%. 3 This error may be significant different in the two cases (polymerization in the absence or presence of thiols). Furthermore, the polyacrylates prepared in the absence of thiol exhibited incomplete solubility and high viscosity of the injected solutions. The filtration was thus difficult and may have led to some shear-degradation. This is attributed to crosslinking due to transfer to polymer followed by termination by combination. The accuracy of the SEC may thus not be high. However, the polyacrylates obtained in the presence of thiol exhibits molecular weight values one order of magnitude lower than that in the absence of thiols. We thus consider this difference to be significant beyond experimental uncertainty.

Table S1: Number-average molecular weights, M n , and weight-average molecular weights, M w , for the thiol (0.4 mol•L -1 ) and non-thiol containing poly(n-butyl acrylates) at various temperatures.

Thermal Analysis

Differential Scanning Calorimetry (DSC)

The glass transition temperature, T g , was obtained for all samples using DSC with a Mettler Toledo Star System. The measurements were done at a nitrogen flow of 30 mL•min -1 , with the following temperature cycle: heating from -100 °C to 150 °C at 10 °C•min -1 , then cooling from 150 °C to -100 °C at 10 °C•min -1 , and finally heating from -100 °C to 150 °C at 10 °C•min -1 . The first heating and cooling steps are used to erase the thermal history of the sample and detect evaporation of little molecules possibly trapped in the samples. The measurements were carried out on the second heating step; the obtained data are listed in Table S3 below.

A decrease in T g by ~20 °C due to the presence of thiol during the polymerization confirms the associated significant decrease in molecular weights also observed above using SEC.

S-4

Thermogravimetric analysis (TGA)

TGA was carried out on a TG 50 Mettler device under a nitrogen atmosphere with the temperature increased from room temperature to 900 °C at 10 °C•min -1 . The decomposition temperature was defined as the temperature at which the sample had lost two percent of its initial mass.

All samples had decomposition temperatures in the range between 300 and 320°C (apart from the sample synthesized at 100°C with thiol, which lost 3.5% of its mass below 300°C, most likely from the evaporation of residual monomer).

NMR Measurements

Sample Packing and Spinning Issues

To get a sample to spin properly under magic-angle spinning (MAS), it is necessary to pack it in a rotor in a homogenous way around the rotor axis. This is particularly challenging with sticky samples like poly (n-butyl acrylate).

In the present work, where sensitivity is sought, it is desirable to pack the samples in large rotors, which increases rotor spinning issues. The poly(n-butyl acrylates) synthesized with thiol were packed in 7 mm rotors. When the sample did not spin well at room temperature, the temperature was increased under slow MAS: above a given temperature, the sample would flow and rearrange homogeneously into the rotor, allowing faster spinning for the 13 C melt-state NMR measurement.

For the poly(n-butyl acrylates) synthesized without thiol at 140 °C, however, this procedure did not function. Even after several hours at high temperature under slow MAS, the sample had not rearranged and MAS frequencies higher than ca 600 Hz were not possible. This was attributed to crosslinking in the sample, which prevents macroscopic flow in the melt (and also limits solubility as seen with SEC). All attempts to pack 7 mm rotors in a homogenous way with this sample failed. In the first attempt, the sample was cooled down with liquid nitrogen to a temperature at which it was flexible but not sticky, cut into small pieces with a scalpel and those pieces were packed into the sample. In another attempt, the sample was packed into the rotor in a home-made device allowing heating the rotor at a controlled temperature: after an hour at 250 °C in air, it had not rearranged but it started becoming yellowish, indicating sample degradation. In the third attempt, the sample was placed in the rotor, swollen with THF, and THF left to evaporate in the fume hood or under vacuum: in the first case, the sample had not rearranged, and in the second case the creation of air bubbles displaced the sample from the rotor.

It was thus decided to pack the poly(n-butyl acrylates) synthesized without thiol in 4 mm rotors, yielding a somewhat lower sensitivity, but allowing faster spinning speeds (the homogeneity of sample packing being less of an issue). All samples could be spun at 9 kHz MAS at room temperature.

Subsequent determination of the precision of the measurements showed that the observed differences were significant and the precision is thus sufficient.

S-6

Experimental Parameters

Measurements were undertaken on a Bruker Avance-II spectrometer (Bruker BioSpin,

Germany) operating at a Larmor frequency of 75.47 MHz for 13 C (300 MHz for 1 H). Quantitative 13 C NMR spectra were recorded at T g +150 °C with single-pulse excitation under magic-angle spinning (SPE-MAS) using a 4 or 5 s 90° pulse, TPPM dipolar decoupling and a 10 s relaxation delay, accumulating 14000 to 17500 transients. Samples synthesized with thiol were measured in 7 mm zirconia rotors with boron nitride caps, at MAS rotational frequencies of 4.5, 3 and 1.8 kHz for increasing synthesis temperatures. Samples synthesized without thiol were measured in 4 mm zirconia rotors with Vespel caps at 9 kHz MAS, because extensive crosslinking prevented their proper spinning in 7 mm rotors. The 13 C chemical shift scale was externally referenced to tetramethylsilane (TMS) at 0.0 ppm using adamantane by setting the CH resonance to 38.5 ppm. 4 Full 13 C chemical shifts assignment

The full chemical shifts assignment is known from literature for both poly(n-butyl acrylate) 5 and 1-octanethiol 6 .

Degrees of Branching for all Samples

Table S3. Glass transition temperature (T g ) and degrees of branching (DB) for the thiol (0.4 mol•L -1 )

and non-thiol containing poly(n-butyl acrylates) synthesized at various temperatures.

T (C) c thiol (mol