1 Communication Letter NMR surface relaxivity in a time -dependent porous

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Communication / Letter

NMR surface relaxivity in a time-dependent porous

system

Neil Robinson, Razyq Nasharuddin, Einar O. Fridjonsson and Michael L. Johns*

Department of Chemical Engineering, The University of Western Australia, 35 Stirling Highway,

Perth WA 6009, Australia

*Corresponding Author:

Professor Michael L. Johns

Chair of Chemical and Process Engineering

The University of Western Australia

Postal Address:

Department of Chemical Engineering

The University of Western Australia

35 Stirling Highway (M050)

Perth WA 6009

Australia

Phone: +61 (08) 6488 5664

Email: michael.johns@uwa.edu.au

Fluid Science and Resources Research Group: www.fsr.ecm.uwa.edu.au

ORCID:

Neil Robinson

0000-0002-0893-2190

Einar O. Fridjonsson

0000-0001-8365-6002

Michael L. Johns

0000-0001-7953-0597

Abstract

We demonstrate an unexpected decay-recovery behaviour in the time-dependent 1H NMR relaxation times of

water confined within a hydrating porous material. Our observations are rationalised by considering the

combined effects of decreasing material pore size and evolving interfacial chemistry, which facilitate a

transition between surface-limited and diffusion-limited relaxation regimes. Such behaviour necessitates the

realisation of temporally evolving surface relaxivity, highlighting potential caveats in the classical

interpretation of NMR relaxation data obtained from complex porous systems.

Main Text

While functional porous materials underpin a vast array of processes of importance to the energy,

environment, chemical and construction sectors, characterisation of key structural and interfacial properties

within such systems is severely hampered by their optically opaque nature. Nuclear magnetic resonance

(NMR) relaxation measurements (also termed nuclear spin relaxation measurements) provide a versatile and

non-destructive approach with which to probe the dynamics of spin-bearing fluids within porous

materials [1,2], and have been applied widely to the study of both equilibrium fluid properties (informing pore

size distributions [3,4], adsorption phenomena [5,6] and diffusive exchange processes [7,8]) and to obtain

time-resolved insight into evolving material structures (such as cements [9–13]). In this letter we expand upon

the established interpretation of NMR relaxation data when probing such time-resolved material properties,

elucidating the uniquely coupled sensitivity of such measurements to the temporal evolution of both pore

structure characteristics and surface chemistry properties simultaneously.

For fluid-saturated porous media, expressions for the dependence of observed 1H (proton) longitudinal ()

and transverse () NMR relaxation behaviour on pore structure and interfacial chemistry are well-known,

taking the general form [14]:





 





(1)

wherein , and where additional terms may be required to fully account for observed  relaxation

rates in the presence of magnetic susceptibly contrast across the solid/fluid interface [15,16]; such effects are

mitigated in this work by performing our measurements at low magnetic field [17]. Here,  are the observed

(measured) time constants and  represent the time constants for the unrestricted bulk fluid. Terms

within parentheses then describe the extent to which pore structure and interfacial chemistry perturb the

observed relaxation characteristics:  is the pore diameter,  is a dimensionless shape parameter (taking

values of 1, 2 or 3 for planar, slit or cylindrical pores, respectively), and  is the self-diffusion coefficient of the

confined fluid. The terms are the (spatially averaged) surface relaxivities of the solid/fluid interface, which

may be modelled as  

 [18], where  are the relaxation time constants within an adsorbed

surface layer of thickness . Such terms describe enhanced rates of relaxation which occur at solid/fluid

interfaces both due to a reduction in molecular mobility within the adsorbed surface layer [19] and through

dipolar proton-electron interactions between adsorbate-bound 1H and paramagnetic species on the pore

surface [14]. Established limiting cases for such relaxation dynamics exist. In the limit  

 for instance,

surface relaxation rates are significantly more rapid than the rates of diffusive transport across the pores, with

Equation (1) reducing to:





 



(2)

Conversely, in the limit  

, diffusion across the pore is sufficiently more rapid than the rates of

enhanced surface relaxation at the pore surface, with Equation (1) reducing to:





 



(3)

Such limits are referred to according to the overall rate controlling process; Equation (2) therefore describes

diffusion-limited relaxation, while Equation (3) describes surface-limited relaxation. Here, we discuss data

which for the first time permits clear identification of a temporal transition between these limiting regimes

within an evolving three-dimensional porous micro-structure.

Figure 1 shows 1H  and  distributions obtained at low magnetic field ( = 0.05 T; (1H) = 2 MHz) for tap

water within the hydrating engineering material cemented paste backfill (CPB) [20–22]. This porous material

comprised a mixture of spherical fly ash particles, minerals tailings, Ordinary Portland cement and water (see

Supplementary Information for extended details of materials preparation), with the solids containing 7.9 wt%,

3.2 wt%, and 2.6 wt% Fe2O3, respectively, as measured by inductively coupled plasma optical emission

spectroscopy (ICP-OES), wherein paramagnetic Fe3+ ions provide the dominant source of relaxation sinks for

adsorbed water at the pore surface. NMR measurements were performed under ambient conditions using

inversion recovery [23] and CPMG (Carr-Purcell Meiboom-Gill) NMR pulse sequences [24,25], respectively,

with the resulting data inverted to produce probability density distributions of observed  and  times via

Tikhonov regularisation [26–28] (see Supplementary Information for extended NMR methods, including

Refs. [29–33]). Acquired  distributions (Figure 1a) show a large primary peak, typical of systems in which

sufficiently slow  relaxation characteristics allow extensive diffusive mixing between water confined within

different pore sizes [34]. Acquired  distributions (Figure 2a), which are naturally more sensitive to local pore

geometry than  due to shorter relaxation times, reveal multiple relaxation environments, indicative of water

confined within a hierarchically porous cement structure. Such distributions are consistent with established

models of cement hydration [35], with the assignment of these relaxation peaks to specific hydrating pore

structures detailed elsewhere [36,37].

Figure 1. Example (a)  and (b)  relaxation distributions for the hydrating material investigated in this study.

Relaxation data was acquired over the first 28 days of material hydration. Colour bars define the probability

density of each relaxation distribution.

In this letter we consider only the modal relaxation times from each inverted distribution, termed  and

, respectively, which are dominated by the most populous pore structures within the hydrating material

under study (capillary pores in traditional cement chemistry notation [38]). In recent work investigating the

hydration behaviour of a similar material in the absence of fly ash particles, a clear mono-exponential

relationship was observed between these modal time constants and hydration time , which defines the

experimental period across which the material is allowed to evolve. This relationship took the form  

 [36], where  are the observed material hydration rates,  provides a scaling factor, and

 are offset parameters necessary to account for non-zero pore sizes at long ; the subscript ‘’ indicates

that surface-limited relaxation is assumed within this system [37]. Fitting  against  then enables the

extraction and comparison of material hydration rates , facilitating quantitative contrast between different

material formulations, preparation procedures, and hydration conditions.

Figures 2a and 2b detail the temporal evolution of our acquired  and  data across 28 days of hydration.

Rather than the expected mono-exponential decay behaviour, however, a clear decay-recovery process

(subscript ‘’) is observed for each data set which may be modelled as:

 



(4)

We rationalise this bi-exponential behaviour through consideration of a transition between the diffusion- and

surface-limited relaxation processes described in Equations (2) and (3). In our chosen material the use of fly

ash introduces a high Fe2O3 content (7.9 wt% as measured by ICP-OES), providing a significantly increased

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1Communication/LetterNMRsurfacerelaxivityinatime-dependentporoussystemNeilRobinson,RazyqNasharuddin,EinarO.FridjonssonandMichaelL.Johns*DepartmentofChemicalEngineering,TheUniversityofWesternAustralia,35StirlingHighway,PerthWA6009,Australia*CorrespondingAuthor:ProfessorMichaelL.JohnsChairofChemicalan...

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