# NMR Relaxometry and IR Thermography to Study Ancient Cotton Paper Bookbinding
## 2 Materials and Methods
### 2d \({}^{1}\)H-Nmr-R  
NMR measurements were performed using an mq-ProFiler (Bruker Biospin, Italy), a single-sided \({}^{1}\)H-NMR probe connected to a laptop. The probe head has a weight of only 2 kg and the portable electronics unit weighs about 10 kg. The probe, working at a Larmor frequency of 17.8 MHz, satisfies the resonant condition within the sensitive volume, an area of about \(2.0\times 0.8\) cm\({}^{2}\) up to a depth of 0.2 cm. To be measured, the sample can be simply placed on the probe surface with no shape or size restriction [5]. In order to proceed with NMR analyses, we ideally subdivided the book front cover into 12 sections (see white grid lines in Figure 1), each one with dimensions \(2.5\times 5.0\) cm and marked as L\({}_{1}\)-L\({}_{12}\). After seven days of previous conditioning in a climatic chamber, we acquired two sets of measures at T = 23 \({}^{\circ}\)C with 45% (i.e., environmental) and 100% relative humidity (RH), respectively. We performed data acquisition in the conditioned environment by placing the sensitive volume of the surface probe at the center of each L\({}_{n}\)-section. The radiofrequency pulse sequence adopted for collecting the correlation between the longitudinal and transverse relaxation times comprised two distinct editing parts, the evolution and the detection period. In each one, the spin system evolved under T\({}_{1}\) and T\({}_{2}\) relaxation mechanisms, respectively. The T\({}_{1}\) and T\({}_{2}\) editing parts arise from a saturation recovery and a CPMG sequence described as [_saturation-_\(\tau_{5}\)-_\(\tau\)_/2-_\(\tau_{E}\)-(\(\pi\)-_\(\tau_{E}\)-_acquisition-_\(\tau_{E}\)-_\(\pi\)_\(R\)_D]m_[3]. In this sequence, \(\pi\)/2 and \(\pi\) indicate the standard radio-frequency pulses, while saturation represents ten \(\pi\)/2 pulses of fixed length and inter-pulse delays geometrically decreased to prevent residual net magnetization at zero evolution time. We acquired the T\({}_{1}\)-T\({}_{2}\) correlated signal by establishing \(\tau_{E}\), i.e., the T\({}_{2}\) encoding time, for different \(\tau_{5}\) that is the T\({}_{1}\) encoding time. The total T\({}_{2}\) encoding time, i.e., 2\(\tau_{E}\)n\({}_{E}\), was set to sample \(\sim\)20 ms of transverse relaxation decay with 2\(\tau_{E}\) = 44 \(\mu\)s and n\({}_{E}\) = 500. To detect a large interval of longitudinal relaxation times, the T\({}_{1}\) encoding was performed ranging \(\tau_{5}\) from 0.1 to 3600 ms, according to a geometric progression with n\({}_{5}\) = 41 different values. We averaged each signal acquisition over m = 1024 scans with a recycle delay time \(\tau_{RD}\) = 2 s for improving the signal-to-noise ratio (SNR). Finally, a phase cycling for the radio-frequency pulses, and the receiver was used [23]. The n\({}_{E}\)\(\times\) n\({}_{5}\) (500 \(\times\) 41) two-dimensional data were processed using the 2D fast Laplace inversion (FLI) algorithm developed by [PERSON] and co-workers [3]. Datasets were elaborated thanks to an optimization method for choosing the proper smoothing coefficient value (\(\alpha_{\mathrm{heel}}\)) that allows balancing the residual fitting error and the noise variance. \(\alpha_{\mathrm{heel}}\) depends on measurements' SNR and on the features of distribution actually required from experimental data. This procedure avoids artifacts arising from too large broadening or excessive separation of NMR signal density peaks. The two datasets, acquired at 45% and 100% RH, were characterized by \(\alpha_{\mathrm{heel}}\)-values within 55 and 90, respectively, along with a relative variation by a factor up to 50 within each group. Usually, a fixed criterion for the choice of the \(\alpha_{\mathrm{heel}}\) enables to compare the correlated distribution functions for different samples, in spite of the differences in the optimal smoothing coefficient. In this study, the moisture contents, rather than the moisture distribution features in the relaxation times space, were preferred for effective comparison of the two RH datasets.