The Open-Access Journal for the Basic Principles of Diffusion Theory, Experiment and Application

Determining the Pore Size Distribution in Synthetic and Building

Materials Using 1D NMR

Sarah Mandy Nagel,1 Christoph Strangfeld,1 Sabine Kruschwitz1,2

1 Bundesanstalt für Materialforschung und -prüfung (BAM), Unter den Eichen 87, 12205

Berlin, Germany 2 Technische Universität Berlin, Straße des 17. Juni 135, 10623 Berlin, Germany

Corresponding author: Sarah Mandy Nagel, Dept. of Nondestructive Testing, Bundesanstalt

für Materialforschung und -prüfung (BAM), Unter den Eichen 87, 12205 Berlin, Germany,

E-Mail: sarah-mandy.nagel@bam.de

Abstract

NMR is gaining increasing interest in civil engineering applications for the use of

microstructure characterization as e.g. pore size determination and monitoring of moisture

transport in porous materials. In this study, the use of NMR as a tool for pore size

characterization was investigated. For our study we used screed and synthetic materials at

partial and full saturation. A successful determination could be achieved when having a

reference or calibration method, although partly diffusion effects have been registered. Due to

these diffusion effects, for the determination of pore size distributions of synthetic materials

another NMR device was needed. Finally, the determination of the surface relaxivity of screed

(50 µm/s) led to a higher value than first expected from literature.

Keywords

NMR relaxometry; pore size distribution; building materials; porous materials; surface

relaxivity

1. Introduction

Due to its high damage potential, the detection of moisture is an important task in civil

engineering especially in the sector “non-destructive testing”. Penetrating water in building

materials is one main cause and driving force for damage processes as e.g. corrosion, mold etc.

To locate moisture damages and to recognize their extents at buildings and constructions,

several non-destructive monitoring methods and handheld devices are applied. Main aspects of

investigations are the resolution of moisture gradients as well as structural changes. However,

to better understand and prevent further material degradations caused by penetrating moisture,

still more expertise about the pore systems and the relevant transport mechanism in porous

systems as e.g. diffusion in building materials is needed.

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

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The method nuclear magnetic resonance (NMR), especially proton NMR relaxometry, is a

suitable method for the detection of moisture because it is highly sensitive to hydrogen protons.

In detail, using NMR relaxation rates of hydrogen protons in dependence of their physical or

chemical bonding can be measured. Furthermore, these relaxation rates are also influenced by

the proton`s environment and therefore the signal also includes information about the pore

system.

Since the late 1970`s, NMR is already applied on cementitious building materials to study

hydration kinetics and pore structure developments [1]. Although NMR was already applied for

example on a fresco using a single-side device, in civil engineering and material research NMR

is still more used in laboratory [2]. Existing devices are less handy instruments and only have

small penetration depths of up to 25 mm. Therefore, NMR is more suitable for applications ex

situ e.g. applications on drilling cores. Nevertheless, NMR especially using a single-side device

enables high resolution of moisture gradients and provides non-destructive information about

pore size distributions at full saturation.

In this work, NMR was mainly applied for investigations in laboratory. The purpose of this

study was the investigation of the applicability of NMR and the restrictions on building and

synthetic materials for the determination of pore sizes and surface relaxivities. Besides full

saturation, the relaxation rates development also at partial saturation of building materials are

regarded. Furthermore, a qualitative estimation of self-diffusion effects due to the used gradient

field was done. Besides screed, also homogeneous synthetic materials have been investigated

e.g. sintered borosilicate glass. For the calibration of the resulting relaxation time distributions

or rather the conversion to pore sizes, results from mercury intrusion porosimetry (MIP) and

surface relaxivity values from literature were used.

2. Methods and Materials

2.1. Methods

The main method used in this study was proton NMR relaxometry [3]. The measurements

were carried out using two different devices of the company Magritek. First, a stray field single

side device called “PM25” or “Mouse” has been applied [4]. This device has a measurement

area of 4 x 4 cm² with a vertical resolution of 120 µm. A special feature is the high precision

lift that enables measurements in varying depths up to a maximum penetration depth of

24.8 mm. Due to the open magnet construction, the device is characterized by a high static

gradient field of about 8 T/m. This gradient strength may influence the relaxation rates e.g.

shifting of relaxation rates because of diffusion effects. The minimum echo time is about 95 µs.

The second used NMR device was the so called “Rock Core Analyzer” (RCA) [5]. The RCA

enables measurements of cylindric samples in a homogeneous field (gradient strength

> 100 mT/m) with an echo time of 300 µs. For the used coil, the possible maximum sample

dimensions were 101.6 mm in diameter and length.

For calibration of the screed samples, MIP results from a measurement campaign of the year

2016 were used [6]. There, screeds of the same type have been measured after hydration

according to the international standard [7]. These measurements have been done using two

devices of the company Thermo Fischer SCIENTIFIC. The device PASCAL 140 was needed

for measurements from 0.1 kPa to 140 kPa. The device PASCAL 400 was utilized for

measurements at high pressure up to the maximum test pressure of 400 MPa. The deduced pore

sizes start from a minimum pore diameter of approximately 2 nm up to 50 µm.

The conversion from NMR relaxation times to pore sizes is applied either using a

comparison method as e.g. MIP or when the material parameter the surface relaxivity is known.

The calculation of pore sizes according to NMR relaxation times can be done with the following

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equation (2.1) [8]:

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𝑇2,Surf= 𝜌 (

𝑆P

𝑉P) = 𝜌

𝑐

𝑅P (2.1)

with 𝑆P

𝑉P⁄ as the ratio of surface area to pore volume; 𝜌 as the surface relaxivity; 𝑅P as the pore

radius and 𝑐 as a shape factor describing the pore model, which is assumed to be 𝑐 = 2 for

cylindrical pore geometry.

This equation results from the simplified transverse relaxation rate due to the neglecting of the

diffusion and bulk term [3, 8]. The component 𝑇2,Bulk is often neglected because in most cases

it is long in comparison to the surface relaxation rate, especially in porous materials. For

simplification, the diffusion term is ignored as well. Due to the estimated small pore sizes and

short relaxation times in building materials as e.g. in screeds, the time-window for possible self-

diffusion effects is expected to be too short. Resulting measurement errors based on this

simplification are assumed to be insignificant.

2.2. Materials and Set-Up

For this study one building material and two more homogeneous synthetic materials have

been investigated. Because many comparison results are available from older measurements,

anhydrite screed was used as a building material. As synthetic materials with a more time

constant and homogeneous pore systems than screed, filter plates made of borosilicate glass

and polyactide pieces were measured. Because of sinter process, borosilicate glass plates with

different pore size distributions could be obtained. Furthermore, polyactide, which is used for

3D printing, was investigated. Polyactide was chosen because it is an alternative material for

the production of special designed NMR calibration probes. The pore sizes of all used materials

as well as the applied methods, are listed in Table 1.

Four brick-shaped screed samples have been produced. They were first measured at the

beginning of hydration (day 3) at almost fully saturated state. Afterwards, the samples were

stored in different climates. In this way, the hydration process is influenced and therefore the

pore system develops differently. The samples A1 and A2 remained saturated in a tank filled

with tap water while samples A3 and A4 were stored in a climate chamber at ambient conditions

of 23°C and 50% rH. That means, that A3 and A4 have been stored under the same conditions

as the screeds samples from the measurements of the year 2016 [6].

To investigate the NMR signal and obtain information about the pore sizes contributing to

the signal at partial saturation, after 1.5 months the samples were resaturated or even reduced

in saturation. For reaching defined partial saturation the samples were stored at different relative

humidities. First, all four samples were stored at 80% rH and 23°C until they reached mass

equilibrium [9]. The next step was the saturation at 90% rH. To complete each stage, the proton

signal of every sample was measured in 9 different penetration depths from 3 to 24.8 mm using

the NMR Mouse. During the entire measurement campaign, the weights have been controlled

using a digital balance with a tolerance according to DIN EN ISO 12571 [9].

As a synthetic material 15 filter plates made of borosilicate glass have been investigated.

Due to sintering, there are three groups with different pore size distributions. The borosilicate

samples are flat cylinders and have a diameter of 70 mm. The height is about 5.5 mm. The size

and format of the samples enable an accurate coverage of the measurement area of the NMR

Mouse and they fit well into the coil of the Rock Core Analyzer. At this point, it must be

explained that measurements using the RCA, which is the property of a different institute, were

not planned from the beginning.

For the measurements with the NMR Mouse, two samples of each group were stacked and

placed into a glass of demineralized water. After two days of saturation, the samples were

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expected to be fully saturated. The samples have a high porosity and the penetrated water does

not seem to be hold within the pores (flowing out could be observed). Therefore, no weight

control was done, and they were measured while staying in the tank of water at a penetration

depth of 10 mm. For comparison, the NMR measurements of the borosilicate glass plates were

repeated using the RCA. The measurements using the RCA were carried out for 3 samples of

each group. Every sample was measured separately at fully saturated state. Due to the device

construction, the samples were measured while being wrapped in a thin plastic foil to prevent

moisture transport and drying. For evaluation, the results within one group were averaged.

The third investigation material was polyactide. Two samples with different structures have

been measured at full saturation (within a tank of demineralized water) using the NMR Mouse.

The measurement depth was 7 mm for both samples. One specimen was characterized by a

honeycomb structure while the second one seemed compact with unknown pore sizes. Later

destructive tests showed, that the second PLA piece included many large voids inside.

Measurements using the RCA were not possible for the PLA samples because they did not fit

into the coil.

Table 1: List of investigated synthetic and building materials, their pore size distributions and the applied methods.

Specimen Pore sizes [µm] Methods

Filter plates

(sintered glas)

Por. 5 1 – 1.6 NMR (Mouse,

RCA) Por. F 4 – 5.5

Por. 4 10 – 16

Polyactide (PLA) 2500 NMR (Mouse)

Anhydrite Screed 1 - 3 MIP, NMR (Mouse)

3. Results

3.1. Relaxation Time Development during Resaturation Process

As described above, four screed samples have been studied using a single side NMR device

at different saturation states. For every measurement the arithmetic mean over the sample depth

was evaluated.

In Figure 1, the transversal relaxation time distributions and their standard deviations at three

different saturation levels are shown. NMR measurements were done at almost fully saturated

state after production and after storage in a climate chamber at 80% and 90% rH. The results

show that a wide relaxation time distribution from 0.001 to 1 s could be achieved at full

saturation (blue). The highest probability could be measured for relaxation times between 0.005

and 0.01 s. Major differences between the single screed samples are not observable.

The results of the partially saturated samples show a different distribution of relaxation

times. In comparison to the saturated state, the relaxation time distributions are significantly

shifted towards lower times around 0.01 down to (the measuring limit of) 0.0001 s. The highest

signal component comes from relaxation times about 0.0004 s. A reduction of the maximum

probability value can also be seen. While the differences between the partial saturation state

after storage at 80% and 90% rH are minor, larger deviations can be observed when comparing

the single screed samples with each other. At both partly saturated states the higher probabilities

are resulting from the samples A1 and A2, which have been stored in a tank of water after

mixing. This observation may be caused by having a higher amount of larger pore sizes than

A3 and A4 due to differences in the pore system development that possibly resulted from their

storage while hydration.

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Due to the arithmetic mean of 9 measurements over the whole sample depths, high standard

deviations resulted. Especially in the range of higher probability values, we measured very high

standard deviations. These might be explained by strong heterogeneities within the screed (e.g.

aggregates and magnetic impurities) and the reducing signal-to-noise ratio with decreasing

water content.

Figure 1: Transversal relaxation time distributions and standard deviations of screed samples at different

saturation levels (arithmetic mean of 9 measurements between 0 and 24.8 mm depth).

3.2. Determination of Pore Size Distribution and Surface Relaxivity

The conversion of relaxation rates to pore sizes of the screed samples was realized using

MIP results as reference. For the calculation, the NMR relaxation times are presented

cumulatively and compared to the MIP results that show the cumulative pore volume over pore

diameter. According to equation (2.1), the parameter surface relaxivity is varied until the curves

fit to the MIP results (see Figure 2). To achieve information about the entire accessible pore

space using proton NMR, every pore needs to be completely filled with water. Therefore, the

use of NMR for the determinations of the complete pore size distribution is only possible at full

saturation.

The pore sizes of the anhydrite screed samples could be determined to reach from 0.03 to

5 µm. The dominant pore sizes are in a range of 0.3 and 2 µm. This result was achieved with a

surface relaxivity of 50 µm/s. In literature, building materials are reported to feature similar

surface relaxivities as natural rocks (determined by comparison with Brunauer-Emmett-Teller

gas adsorption (BET) results to lay between 0.5 and 10 µm/s) [10, 11]. Dalas et al. (2014)

investigated the surface relaxivities ρ2 of cement hydrates and determined values in a range of

1 to 6 µm/s [11]. The only component reaching higher surface relaxivities up to 44.7 µm/s is

the mineral ettringite which is therefore assumed to have an influence on the resulting total

surface relaxivity of the investigated screed samples.

The relaxation time distributions measured at partial saturation are also presented in Figure

2. Assuming that the material composition does not significantly change due to late hydration,

a conversion to pore sizes was done using the same surface relaxivity value. In this case, we

assume that only smaller pores remain saturated and contribute to the NMR signal, whereas

larger pores are partly saturated or completely emptied [12].

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Figure 2: Pore size distributions as obtained with MIP and NMR (ρ = 50 µm/s) on screed samples at different

saturation levels (arithmetic mean of 9 measurements between 0 and 24.8 mm depth).

The next step of investigation was the pore sizes determination of borosilicate glass plates

using NMR data and a surface relaxivity value from literature for conversion. As it can be seen

in Figure 3, all measurements that were done with the NMR Mouse show the same distributions

(solid lines). The results show wide distributions from 0.1 to 2 µm for all three specimens that

additionally do not fit the manufacturer’s specifications (see Table 1).

A repetition of measurements using the RCA device (homogeneous field) led to different

results (see the dashed lines in Figure 3). Using the surface relaxivity value from Mohnke

(2014) [13], the determined pore sizes distributions agree with the manufacturer’s

specifications for the specimen P5 and PF. Having the largest pore sizes up to 16 µm, only for

the specimen P4 there was a slight underestimation.

Figure 3: Pore size distributions of borosilicate glass plates calculated from NMR data using a surface relaxivity

of ρ = 1.8 µm/s [13].

At last, the relaxation times of the PLA samples in Figure 4 show a similar distribution as

the pore size distribution of the borosilicate glass plates when measured with the NMR Mouse.

An additional comparison of pure water measurements clarifies that the hydrogen signal within

the PLA samples is the same as of pure water. As the PLA samples, especially the honeycomb

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structured sample, have large pores or rather voids, the relaxation times are the same as for pure

water. And although the compact PLA sample seemed nonporous, the measurements led to the

same relaxation time distribution but with lower probability (solid lines in Figure 4). A later

split revealed large voids inside the sample.

A comparison with pure water measurements using the RCA proofed that the relaxation

times of the PLA samples and pure water measured with the single side device seem shifted

due to possible diffusion effects. As already known, the transverse relaxation time of water lays

in the range of seconds (dashed line in Figure 4).

Figure 4: Transverse relaxation time distributions of compact and honeycomb PLA compared to pure distilled

water.

4. Discussions

The results presented above show that a successful determination of pore sizes is strongly

depending on the materials parameter as e.g. the surface relaxivity and pore sizes itself.

Furthermore, technical aspects as the used device play a significant role. For a determination of

pore sizes from NMR data in general, either the material parameter the surface relaxivity has to

be known or a calibration method is applicable.

For the measurements on screed samples resulted a surface relaxivity higher than expected.

On the one hand, the authors see the reason for smaller deviations in the choice of the

comparison method. As described in Borgia et al. (1996) [10], ρ depends on the resolution of

the chosen method. Therefore, it is known that MIP is more an approved tool for pore throat

size determination [14]. On the other hand, as already mentioned above an explanation for a

higher value could be the influence of single hydration components as e.g. the mineral ettringite.

Due to the given sulfate in the screed a crystallization of ettringite can be assumed. One

additional reason could be the reference results from older measurement campaigns, that maybe

do not fit due to smaller differences during the hydration processes.

Another aspect that could be recognized in Figure 2 is the interpretation of relaxation times

at partly saturated state. The distinction of proton signal between fully saturated smaller pores

and partly saturated larger pores is still not clear. Lower relaxation times could be caused by

both cases, but a clear differentiation is not possible. Furthermore, the cases of partial saturation

often are not considered in many pore model representations. Therefore, also the validity and

variation of surface relaxivity is unsure at partly saturated state.

Finally, one important observation were the shifts to lower relaxation times during

measurements of the synthetic materials using the NMR Mouse (see Figure 3 and Figure 4). In

comparison to the measurements with the RCA, it can be assumed that the measurements failed

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due to diffusion effects caused by the gradient field (8 T/m) of the NMR Mouse and long

relaxation rates. These diffusion effects may have occurred due to longer relaxation times

resulting from larger pore sizes and a low interaction rate of hydrogen protons with their

environment. Furthermore, chemical composition and material parameter as the surface

relaxivity itself are assumed to have any influence on the resulted effects. In this case, the

simplification of equation (2.1) is incorrect because the influence of the diffusion term was still

measurable and significant. This knowledge is important for further studies. It must be clarified

if and how these effects can be corrected and rather they can be used for getting information

about microstructures.

In general, it must be said that this study represents a good base for further experiments using

the NMR Mouse. Especially, the measurements on screed need repetitions and new resaturation

to neglect any influences of hydration. Furthermore, a control of pore sizes of the borosilicate

glass plates by doing MIP and gas adsorption is planned.

5. Conclusions

In this study, NMR was applied to building and synthetic materials with the main goal of

inferring pore size determinations. Besides, possible influences as well as sources of error

depending on the chosen material and preparation have been investigated. The determination

of pore size distributions on hydrating screeds in this study has been quite successful. We

observed higher surface relaxivity values than expected of about 50 µm/s which might be

influenced by hydrating components like ettringite. However, the behavior of the surface

relaxivity at partly saturated state and during hydration processes requires more investigations.

A clear distinction of the proton signal at partly saturated states also remains still an open

question.

In this work, the measurements with the NMR Mouse on synthetic materials were falsified

due to occurring diffusion effects while measuring within the existing magnetic gradient.

Especially, when comparing the results with measurements of pure water the effects were very

striking. Further studies require a better quantification of these effects and possible corrections.

In conclusion, it can be said that NMR, depending on the investigation material and the

technical aspects of the used device, is suitable for special applications according to e.g. pore

space characterization in civil engineering. Although mostly applied in laboratory, NMR has a

high potential for non-destructive resolution and characterization of moisture transport and the

relevant material parameters.

Acknowledgment

The authors want to thank Dr. Stephan Costabel and Ludwig Stelzner for the scientific

advises as well as inspiring discussions. For the provision of the user-friendly NMR inversion

algorithm the authors are grateful to Dr. Thomas Hiller. Furthermore, the authors are thankful

to Dr. Raphael Dlugosch and Cornelia Müller for the support and the possibility to use the NMR

device at the LIAG.

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