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The inversion of two-dimensional NMR Relaxation data requires the solu- tion of a őrst-kind Fredholm Integral equation with separate exponential kernels. We extend to two-dimensions the Uniform Penalty principle (Borgia et al. J. Magn. Res- onance, 1998) by proposing an algorithm based on Tikhonov regularization with local regularization parameters and nonnegative constraints. The local regularization terms are computed as the ratio between noise norm and a combination of local curvature and gradient values. The corresponding regularization problem is solved by Projected Newton iterations. Experiments show better reconstructions of peaks and ŕat areas compared to Tikhonov regularization with global regularization parameter.

Nuclear magnetic resonance (NMR) has provided us with many beneficial opportunities for science and technology. Its continued use in novel fields has yielded impressive strength and attractiveness for nearly a century. This is particularly true with regards to the topic of this book, the exploration of ‘‘Fluid Transport in Porous Solids and Heterogeneous Materials’’. Here, the benefit of NMR in being able to look ‘‘from the outside’’ into a system becomes particularly evident. NMR operates as an ‘‘ideal spy’’, providing information without interfering with internally occurring phenomena. NMR is able to give information on pore spaces as well as anything that might happen within them. This wide-range of information that is accessible is illustrated by the examples in this book. The origin of some of these developments can, most remarkably, be traced back over many decades, to the very beginning of NMR research. In this chapter we will recollect some of the roots of the challenges we face today with applying NMR to studying ‘‘Fluid Transport in Porous Solids and Heterogeneous Materials’’- albeit with some bias by personal experiences and impressions.

Soil remediation has recently included the use of organic recycled materials (e.g. sewage sludge or paper mill sludge) which, thanks to their stability in aerobic conditions, can improve soil properties. Paper sludge, for example, adds nutrients to a poor Organic Matter (OM) soil, since the Total Organic Carbon (TOC) content is generally high. TOC and TOCto-Nitrogen ratio (TOC/N) and other chemical elements (P, Ca,Mg, Na and K) are generally used to characterize amended soils [1]. It has been recently observed that the quantity of OM can influence soil texture and consequently the pore size distribution. New efforts are arising towards the use of non-invasive and non-destructive techniques to characterize this kind of sample, to gain more reliable information on interactions between OM and soil mineral phases. Proton Time-Domain Nuclear Magnetic Resonance (1H TD-NMR) can be profitably employed to investigate the textural properties of these amended environmental substances. Applications of the TD-NMR technique are not so much used in soil science, although it shows great potential, probably due to the huge heterogeneity of these materials and to the presence of high paramagnetic ion concentrations found both in natural soils and in the contaminants. In particular, in this study contaminated soils have been characterized by T1 distribution analysis, using a specifically developed NMR sequence to overcome experimental difficulties, to obtain information on the porosity related to the irreducible water [1]. On the other side, N2 sorption at soils surfaces has been usually used for the determination of the Specific Surface Area (SSA). SSA depends on the structure of soil aggregates and permits one to investigate OM-soil minerals aggregation [2]. In this work we investigate how the amount of TOC in soil sample can be investigated by TD-NMR and SSA techniques. [1] M. Vannini, A. Bonoli, V. Bortolotti, P. Macini, E. Mesini. Proceedings of the 3rd International Conference on industrial and hazardous waste management, Chania (Crete), September 2012. [2] R. Wagai, L. Mayer, K. Kitayama, Geoderma, 149 (1-2), 152-160, (2009).

In the framework of the European Project CoralWarm [1,2], the pore-volume structure of the skeletons of scleractinian corals from Mediterranean Sea have been analyzed with the aim to determine parameters from NMR Relaxometry useful to relate porosity and pore-size distribution to environmental conditions. The final goal is to relate structure variations to climate change. Mercury intrusion porosimetry shows wide ranges of pore radius, but the high Hg pressure could cause particle compression and rupture. The definition of a method to determine porosity and pore-size distribution in a non-invasive, non-destructive way can be of great interest. In a recent paper [3] we have demonstrated that NMR Relaxometry of clean coral skeletons, saturated with water, is an efficient tool for pore-volume structure characterization. The data obtained from CPMG sequence were inverted by UpenWin software [4] to get T2 distributions. Parametric and non-parametric statistical test have been performed on two parameters extracted from T2 distributions: the cut-off time (relaxation time in between two peaks, or the tail and the peak) and the micro-porosity (fraction of signal with relaxation times below the cut-off). Also, a multivariate analysis has been performed to check the sensitivity of microporosity to variations of mass and growing temperature. The results demonstrate that the NMR parameters so determined are good tools to check the sensitivity of the corals to the environmental changes. Acknowledgements: the research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement n° 249930 –CoralWarm: Corals and global warming: the Mediterranean versus the Red Sea; the authors wish to thank the CoralWarm team members for corals sampling and cleaning. [1] ERC, IDEAS Project CoralWarm - Corals and global warming: the Mediterranean versus the Red Sea, http://www. coralwarm.eu.; [2] E. Caroselli et al., Zoology, 114, 255-264 (2011); [3] P. Fantazzini et al., Environmental Science & Technology, in press, DOI:10.1021/es402521b; [4] UpenWin, a software to invert multi-exponential data, commercialized by the University of Bologna, www.unibo.it/Portale/Servizi+ImpreseUpenWin.htm.

The collection and composting of organic waste both from families and from industrial production processes are considered as good practices for waste management. Composts made from sewage sludge, household waste, straw, bark, have successfully been employed in gardens, pot cultures, arable land, and even in forests. In general, composts contribute to the structure and nutrient supply of soils or artificial substrates for plant growth. Compost chemical and microbial properties, which define compost maturity, are important key factors for correct use in environmental and agricultural activities. Parameters such as the temperature, pH and C/N ratio can be observed to monitor the compost maturation and to decide on the compost quality and stability [1]. Proton Nuclear Magnetic Resonance relaxometry (1H-NMR) can be used to follow compost biodegradation during time, as it permits the monitoring of internal compositional and structural modifications, as already observed in many food types when they experience natural or not natural processes [2]. Since generally the parameters of biodegradation are volume averaged and little is known on the influence of local behaviour on the final overall biodegradation, a local investigation of the compost mixture is desirable [3]. Quantitative Relaxation Tomography (QRT), which gives spatial information on relaxation times combining 1H-NMR relaxometry with Magnetic Resonance Imaging, can be an innovative tool to monitor compost degradation and maturation. In this work a sample of compost has been monitored for two months by means of both T1 and T2 QRT maps [4]. In a first preliminary analysis, both kinds of maps seem to well describe a trend that follows the three phases of the composting process: mesophilic, thermophilic and maturation, moreover having information of the spatial distributions of these phases. [1] J. Forster, W. Zech, E. Wiirdinger, Biology and Fertility of soils, 16, 93-99, (1993). [2] M. F. Marcone, S. Wang, W. Albabish, S. Nie, D. Somnarain, A. Hill, Food Research International, 51(2), 729-747, (2013). [3] F. P. Duval, S. Quellec, A. Trémier, C. Druilhe, F. Mariette, Waste management, 30(4), 610-619, (2010). [4] G. C. Borgia, V. Bortolotti, P. Fantazzini, journal of Applied Physiscs, 90(3), 1155-1563, (2001).

The internal distribution of water-repellent products applied to surfaces to make a porous material repellent is of great interest in the field of the safeguard of cultural heritage items such as stone buildings, statues and frescos. Water is the main cause of degradation of porous materials exposed to rain, moisture and air pollutants. In previous papers[1], it has been shown how MRI allows one to evaluate and compare the performance of products and treatments used. Those products were commercial ones, made for different uses than cultural heritage items protection. In the middle of the ‘80s, the group of CNR in Florence started to synthesize mono-biand tetra-functionalized perfluoropolyetheric compounds for the specific use in the protection of stone, with the following properties: (i) stable to chemical agents, heating and UV irradiation; (ii) high water-repellency; (iii) ability to perform treatments in such a way that the natural permeability of stone to air and water vapor is not significantly reduced; (iiii) chemically inert with the stone substrate, and therefore completely reversible. Unfortunately, the best products synthesized were soluble in Chlorofluorocarbons. Now, new products containing a perfluoropolyetheric and hydro-alcoholic solvents, but not soluble in water or Chlorofluorocarbons. Their hydrophobic and penetration properties have been investigated by MRI images, taken on biocalcarenite samples treated with commercial and new fluorinated compounds, at increasing times during capillary water absorption. The presence of water inside each sample could be visualized and the height reached by the wetting front quantified as a function of time. The images were analyzed by an in-house software able to identify the front by an objective criterion. The images show the different protection efficiency of products and treatments. Good fits to the data were obtained with theoretical and empirical models of absorption kinetics, starting from the Washburn model. The data analysis gives us parameters useful to quantify the effects of the treatments on the capillary properties. The results demonstrate the better performance of the new fluorinated compounds able to preserve stones and environment. [1] M. Gombia et al., J Appl Phys, 103, 094913 (2008).