Responsive Adsorption of N-Isopropylacrylamide Based Copolymers on Polymer Brushes

We investigate the adsorption of pH- or temperature-responsive polymer systems by ellipsometry and neutron reflectivity. To this end, temperature-responsive poly (N-isopropylacrylamide) (PNIPAM) brushes and pH-responsive poly (acrylic acid) (PAA) brushes have been prepared using the “grafting onto” method to investigate the adsorption process of polymers and its reversibility under controlled environment. To that purpose, macromolecular brushes were designed with various chain lengths and a wide range of grafting density. Below the transition temperature (LCST), the characterization of PNIPAM brushes by neutron reflectivity shows that the swelling behavior of brushes is in good agreement with the scaling models before they collapse above the LCST. The reversible adsorption on PNIPAM brushes was carried out with linear copolymers of N-isopropylacrylamide and acrylic acid, P(NIPAM-co-AA). While these copolymers remain fully soluble in water over the whole range of temperature investigated, a quantitative adsorption driven by solvophobic interactions was shown to proceed only above the LCST of the brush and to be totally reversible upon cooling. Similarly, the pH-responsive adsorption driven by electrostatic interactions on PAA brushes was studied with copolymers of NIPAM and N,N-dimethylaminopropylmethacrylamide, P(NIPAM-co-MADAP). In this case, the adsorption of weak polycations was shown to increase with the ionization of the PAA brush with interactions mainly located in the upper part of the brush at pH 7 and more deeply adsorbed within the brush at pH 9.

If the dry layer is considered to contain only polymer chains, the volume occupied by a single chain (Nb 3 ) can be calculated from the following relation: where D is the average distance between two anchoring sites,  is the grafting density or the number of chains per unit area,  PNIPAM = 1.10 g cm -3 is the density of PNIPAM, M n the number-average molar mass of the polymer, N corresponds to the number of monomers per chain or the degree of polymerization and b 3 is the size of a monomer.
The grafting density can be calculated from the dry thickness measured by ellipsometry and the molar mass M n determined by SEC: The distance between two anchoring chains is an important parameter that defines the conformation regime: the "mushroom regime", where D is higher than twice the radius of gyration of a free polymer chain (R 0 ), and the "brush regime" for D < 2R 0 . In the brush regime, polymer chains are densely packed so that they have to stretch in the direction normal to the substrate and cannot take an isotropic conformation as for free chains.
Consequently, the scaling laws representing the swelling or collapse of polymer brushes in good or bad solvent conditions are different from those of free polymer chains. In order to calculate the size of a free chain in well-defined solvent conditions we have used the quantitative definitions given for non-solvent (dry state) and solvent: where C ∞ = 10 is the characteristic ratio of PNIPAM [1] and l = 1.54 Å, the carbon-carbon bond length.
We have to consider that at 20 °C the PNIPAM chain is in rather good solvent conditions, i.e.
well above the -conditions, and the real size of the chain should be higher that its unperturbed dimension. Similarly, in the collapsed state, the PNIPAM chain could keep water molecules in its pervaded volume and its real size should be larger than in the dry state. Nevertheless, even if we consider that the globular chain contains about 50 wt% of water, as we will see later, its size will be only 25% higher compared to the dry state.

Determination method of the volume fraction of monomers by neutron reflectivity
Neutron reflectivity was used to study PNIPAM brushes in water. This technique is sensitive to the scattering length density profile normal to the surface Nb(z) and thus to the profile of the volume fraction of monomers (z). The specular reflection does not allow the distinction between the roughness and the inter-diffusion of a layer if the size of heterogeneities is smaller than the coherent length of neutrons (which is about a few microns). Lateral morphologies of PNIPAM brushes determined by AFM shows that the size of the aggregates is lower than 50 nm in the plane and the layer roughness (precisely the root-mean-square deviation of the surface) is a few nanometers, as also observed by Bittrich et al. [2] It means that the average thickness and the volume fraction profile of PNIPAM brushes can be determined unambiguously in spite of the in-plane irregularities. Figure 1 shows an example of neutron reflectivity data and the profile of the volume fraction of monomers corresponding to the best fit of the experimental results. For this sample of PNIPAM brush (M n = 121 kg.mol -1 and σ = 0.078 nm -2 ) measured at 20 °C, the reflectivity curve does not display obvious Kiessig fringes and the density profile is consistently smooth or gradual. The smoothly decaying profile is in agreement with mean-field calculations which predict analytical (parabolic or tanh-derived) functions for the volume fraction profiles [3][4][5][6].
According to the step profile used to fit the experimental data, the conformation of chains is unfortunately limited as the chain ends should be at the same distance from the surface. A soft profile provides more flexibility since all the chains, even attached, have not necessary the same stretching and the extremities of chains can be at any distance from the surface.
Moreover, the polydispersity of chains can also be taken into account using an additional component (exponential queue for example) to the main parabolic profile. The analytical forms of the density profile of polymer brushes were investigated in details in previous publications and in particular for poly(acrylic acid) brushes [7]. In the present work, where we aim at comparing the density profiles of polymer brushes at different temperatures, with or without adsorbed polymers, a simple step model is well adapted.

Swelling ratios of PNIPAM brushes
Note that the inverse of the swelling ratio, /L, corresponds to the average volume fraction of polymer in the swollen layer. From a theoretical point of view, the swelling ratio of polymer brushes can be estimated on the basis of scaling relations. Starting from equation [S1], a first relation between the dry thickness  and the grafting density  can be extracted: The swollen thickness L of neutral polymer brushes in good solvent is given by Alexander-de Gennes scaling law [8][9][10] : The same argument will give L  Nb 2  1/2 in -conditions and L  Nb 3  in bad solvent conditions. Finally, the swelling ratio can be obtained by coupling equations [S4] and [S5]: with β = -2/3, -1/2 and 0 for good, and bad solvents, respectively.

Note that equation [S6] is strictly valid if the ratio of the monomer size in the swollen brush
to that in the dry brush is independent of the grafting density. This condition was met for all the brushes in the range of grafting density investigated. As proof, the distance between two attached chains (D = 17 Å for the lowest) is in all cases much higher than the monomer size Accordingly, experimental swelling ratios obtained with polymer brushes of different molar masses have been plotted in Figure S2 versus their grafting density.
Grafting density (nm Contrary to the swelling ratio (L 20 /γ), no physical meaning is expected for the scaling exponent of L 20 /L 60 versus the grafting density as this variation takes into account the fraction of water in the brush which varies with the molar mass of PNIPAM chains. Indeed, the average volume fraction of water in the collapsed brushes (1- 60 ; see Table 2) varies from 40 to 50 % for brushes prepared with M n = 70-121 kg mol -1 and up to 70 % for the brush grafted with M n = 11.9 kg mol -1 . It is also worth mentioning that in this last case, the thickness and then the swelling of the polymer brush remains almost unchanged between 20 and 60 °C (no deswelling).
Retrospectively, it is now possible to calculate the size of free PNIPAM chains at 20 °C as we know the thickness of the swollen layer and we have shown that water is a good solvent at this temperature. For that purpose we will consider that each polymer chain inside the brush self-organize into an array of correlation blobs perpendicular to the surface. If g is the number of monomers per correlation blob and N the total number of monomer per chain, we have in good solvent conditions: [10] and where A is a common prefactor and V F 1/3 is the Flory radius, i.e. V F is the pervaded volume of an isolated polymer chain in good solvent conditions. As the number of correlation blobs (N/g) can be calculated from the swollen thickness of the polymer brush (N/g=L/D), then it comes: As expected from theoretical predictions (equations [S3] and [S8]), we can see in Table S1 that free PNIPAM chains swell in good solvent (V F   ) and in good solvent V F 1/3 . V F /L 20 D 2 is the overlapping ratio of PNIPAM chains inside the brush and φ 20 their volume fraction.