4 5The self-diffusion coefficients of different molecular weight PEGs (Polyethylene glycol) and casein 6 particles were measured, using a pulsed-gradient nuclear magnetic resonance technique (PFG-NMR), in 7 native phosphocaseinate (NPC) and sodium caseinate (SC) dispersions where caseins are not structured 8 into micelles. The dependence of the PEG self-diffusion coefficient on the PEG size, casein 9 concentration, the size and the mobility of casein obstacle particles are reported. Wide differences in the 10 PEG diffusion coefficients were found according to the casein particle structure. The greatest reduction 11 in diffusion coefficients was found in sodium caseinate suspensions. Moreover, sodium caseinate 12 aggregates were found to diffuse more slowly than casein micelles for casein concentrations > 9 g/100 g 13 H 2 O. Experimental PEG and casein diffusion findings were analyzed using two appropriate diffusion 14 models: the Rouse model and the Speedy model, respectively. According to the Speedy model, caseins 15 behave as hard spheres below the close packing limit (10 g/100 g H 2 O for SC (Farrer & Lips, 1999) and 16 15 g/100 g H 2 O for NPC (Bouchoux et al., 2009)) and as soft particles above this limit. Our results 17 provided a consistent picture of the effects of diffusant mass, the dynamics of the host material and of 18 the importance of the casein structure in determining the diffusion behavior of probes in these systems. 19 20

Pulsed field gradient nuclear magnetic resonance and proton nuclear magnetic resonance relaxometry were used to study the self-diffusion coefficients and molecular dynamics of linear (PEGs) and spherical probes (dendrimers) in native phosphocaseinate suspensions and in a concentrated rennet gel. It was shown that both the size and the shape of the diffusing molecules and the matrix topography affected the diffusion and relaxation rates. In suspensions, both translational and rotational diffusion decreased with increasing casein concentrations due to increased restriction in the freedom of motion. Rotational diffusion was, however, less hindered than translational diffusion. After coagulation, translational diffusion increased but rotational diffusion decreased. Analysis of the T₂ relaxation times obtained for probes of different sizes distinguished the free short-chain relaxation formed from a few monomeric units from (i) the relaxation of protons attached to long polymer chains and (ii) the short-chain relaxation attached to a rigid dendrimer core.

The dynamics of rigid dendrimer and flexible PEG probes in sodium caseinate dispersions and acid gels, including both translational diffusion and rotational diffusion, were studied by NMR. Above the onset of the close-packing limit (C ∼ 10 g/100 g H2 O), translational diffusion of the probe depended on its flexibility and on the fluctuations of the matrix chains. The PEG probe diffused more rapidly than the spherical dendrimer probe of corresponding hydrodynamic radius. The greater conformational flexibility of PEG facilitated its motion through the crowded casein matrix. Rotational diffusion was, however, substantially less hindered than the translational diffusion and depended on the local protein-probe friction which became high when the casein concentration increased. The coagulation of the matrix led to the formation of large voids, which resulted in an increase in the translational diffusion of the probes, whereas the rotational diffusion of the probes was retarded in the gel, which could be attributed to the immobilized environment surrounding the probe. Quantitative information from PFG-NMR and SEM micrographs have been combined for characterizing microstructural details in SC acid gels.