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Conduction, relaxation and complex impedance studies onPortland cement mortars during freezing and thawing

Citation for published version:Kim, J, Suryanto, B & McCarter, WJ 2019, 'Conduction, relaxation and complex impedance studies onPortland cement mortars during freezing and thawing', Cold Regions Science and Technology, vol. 166,102819. https://doi.org/10.1016/j.coldregions.2019.102819

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Download date: 04. Feb. 2022

Accepted Manuscript

Conduction, relaxation and complex impedance studies onPortland cement mortars during freezing and thawing

Jaehwan Kim, Benny Suryanto, W. John McCarter

PII: S0165-232X(19)30067-9DOI: https://doi.org/10.1016/j.coldregions.2019.102819Article Number: 102819Reference: COLTEC 102819

To appear in: Cold Regions Science and Technology

Received date: 2 February 2019Revised date: 3 May 2019Accepted date: 28 June 2019

Please cite this article as: J. Kim, B. Suryanto and W.J. McCarter, Conduction, relaxationand complex impedance studies on Portland cement mortars during freezing and thawing,Cold Regions Science and Technology, https://doi.org/10.1016/j.coldregions.2019.102819

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Conduction, relaxation and complex impedance studies on Portland cement

mortars during freezing and thawing

Jaehwan Kim, Benny Suryanto* b.suryanto@hw.ac.uk, W. John McCarter

School of Energy, Geoscience, Infrastructure and Society, Institute for Infrastructure and

Environment, Heriot Watt University, Edinburgh, EH14 4AS, Scotland, U.K.

*Corresponding author.

ORCID:

Benny Suryanto: 0000-0002-3979-9994

William John McCarter: 0000-0002-1949-2856

Abstract

The influence of freezing and thawing on the complex electrical impedance of Portland

cement mortars is presented with measurements obtained over the bandwidth 20Hz–1MHz.

Samples were exposed to a cyclic temperature regime within the range -70C – +20C. In

addition to Nyquist plots, the bulk conductivity and permittivity were de-embedded from the

impedance measurements and presented in the frequency domain to study ice

formation/thawing, and its influence on conduction and polarization processes within the

capillary and gel pore network. The activation energy for bulk ionic conduction and

polarisation processes was also established using an Arrhenius relationship and it was shown

that hysteresis was present over a significant portion of the thermal cycle. Where hysteresis

effects were present, the conductivity of the sample was lower on thawing portion of the

cycle than on the freezing. It was also shown that when the bulk conductivity was presented

in an Arrhenius format, four distinct regions were identified on the cooling part of the cycle,

whereas on the heating part of the cycle only two regions were present. It was found that the

contribution of dissipative conduction processes to the overall conduction increased with

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decreasing temperature and with increasing frequency. The water/cement ratio is shown to

have a significant influence on complex impedance measurements, the depression in freezing

and melting point of the pore-water and activation energy.

Keywords:

Mortar; Freezing and Thawing; Complex Impedance; Conductivity; Permittivity; Arrhenius;

Hysteresis Effects; Activation Energy.

1. Introduction

The micro-porous nature of cement binder and environmental exposure conditions have a

significant influence on the long-term durability of concrete. In cold regions, the action of

freeze/thaw cycles can be particularly deleterious when the concrete remains in a saturated

state. As the pore-water within concrete freezes, it expands and can cause internal cracking

and surface scaling, both of which have a considerable impact on the long-term performance

of concrete (Beaudoin and MacInnis, 1974; Du et al., 2019; Liu et al., 2014; Ren et al., 2019;

Sicat et al., 2013; Tian and Han, 2018; Zhang et al., 2017). In a porous material such as

concrete, it is recognised that the temperature at which the pore-water freezes is dependent

upon several factors, including the moisture-state of the concrete (viz, the degree of pore

saturation), ionic concentrations within the pore-water and the microstructure of the capillary

pore-system within the cementitious binder (Esmaeeli et al., 2017; Farnam et al., 2015; Wang

et al., 2014). Regarding the latter, microstructural features which have a direct influence of

freezing and thawing include pore-size, pore-size distribution, pore constriction, pore

connectedness and pore tortuosity.

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To date, a variety of pore characterisation techniques have been developed and exploited by

various researchers, ranging from mercury intrusion porosimetry (Sun and Scherer, 2010) and

water/gas absorption (Sun and Scherer, 2010; Zeng et al., 2014) to more sophisticated

techniques such as small-angle neutron scattering (White et al., 2017), nuclear magnetic

resonance (Mitchell et al., 2008), and X-ray computed tomography (Tian and Han, 2018).

Some of the techniques employ a thermodynamic approach using the Kelvin or Gibbs–

Thomson equation to determine pore-structure information based on the freezing/melting

point depression of the pore fluid or the volumetric ratio of frozen water. Such techniques

include,

(a) thermoporosimetry, which employs the heat-flow from exothermic water-freezing and

endothermic water-melting within the cement matrix (Brun et al., 1977; Kjeldsen and

Geiker, 2008; Sun and Scherer, 2010);

(b) nuclear magnetic resonance cryoporometry, which utilises the melting-point depression

of the pore-water to determine pore size distribution (Mitchell et al., 2008);

(c) relaxometry, which determines pore diameter based on the enhanced relaxation of

water molecules at the pore surface (Cohen and Mendelson, 1982; Gallegos et al.,

1988);

(d) ultrasonic porosimetry, which uses the difference in the velocity of longitudinal

compression waves in the liquid and ice phases as a measure of ice content (Fabbri et

al., 2009, 2006);

(e) dielectric techniques, which take advantage of the difference in the dielectric properties

of liquid and frozen water as an estimate of ice content (Fabbri et al., 2006; Fabbri and

Fen-Chong, 2013); and,

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(f) electrical property measurements, which utilizes the bulk ionic conductivity (or its

reciprocal, resistivity) of the porous material to study freezing/thawing (McCarter et al.,

2015a; Perron and Beaudoin, 2002; Sant et al., 2011; Sato and Beaudoin, 2011; Wang

et al., 2014; Wang et al., 2016; Tomlinson et al., 2017).

Monitoring the electrical properties of cementitious materials has gained increasing interest

due to it being non-destructive and technically simple to perform; in addition, samples are not

limited to cement pastes, but mortars and concretes can also be studied (Suryanto et al.,

2017). Further to (f) above, electrical measurements have been exploited as a means of

estimating the pore-neck and pore-cavity radii of a wide range of concrete mixes (McCarter

et al., 2015a); the volumetric ratio of ice within cement mortars (Wang et al., 2016); the

activation energy of cementitious materials and phase changes (Farnam et al., 2015;

Tomlinson et al., 2017); the formation factor (Sant et al., 2011) and the degree of

microstructural damage due to repeated freeze/thaw cycles (Perron and Beaudoin, 2002; Sato

and Beaudoin, 2011; Wang et al., 2014).

Despite these advancements, studies are limited with respect to the format of data

presentation, the frequency at which electrical measurements are taken and the temperature

range employed, in particular the low temperature limit. Regarding the latter, studies have

been taken over the temperature range -30 to +70oC at 1 kHz (McCarter et al., 2015a); -28

oC

to +10oC at 1kHz (Wang et al., 2016); -24

oC to +24

oC at 10kHz (Tomlinson et al., 2017;

Giatec) and -35oC to +23

oC, with measurements taken over the frequency range 0.1Hz–

10MHz (Farnam et al., 2015). In these studies, a two-point electrode configuration was

employed; however, a four-point configuration has also been used, although the lower

temperature limit is also restricted to -30oC (Wang et al., 2013; Wang et al., 2014).

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Given the clear link between pore-size and the freezing/melting point of pore-water extending

the temperature to a lower range could establish an improved understanding of the process of

ice formation within the entire pore system which comprises both capillary pores and gel

pores. The only study to date which covers a wide temperature range (-80 o

C to +20oC) and

frequency (100Hz–5MHz) is that on cement pastes by Perron and Beaudoin (2002) and Sato

and Beaudoin (2011). However, data presentation could be further exploited to allow a better

understanding of microstructural features on ice formation and forms the main focus of this

current study.

Results are presented from the simultaneous monitoring of both the temperature and electrical

impedance of Portland cement mortars at three different water/cement ratios. The samples

were subjected to a freeze/thaw regime within the temperature range -70oC to 20

oC, with

electrical measurements undertaken within the frequency range 20Hz–1MHz. Measurement

results are presented in a range of formalisms to aid interpretation, including Nyquist plots,

frequency domain behaviour of conductivity and permittivity, Arrhenius relationships and

activation energies for conduction and polarization processes during ice formation and

melting. The focus of the present work is to highlight the nature of these processes over the

extended range of temperature and frequency.

2. Experimental programme

2.1 Material, test sample and fabrication

Mortar samples (50×50×50 mm) were made with ordinary Portland cement (CEM I 52.5N) to

BS EN 197-1 (British Standards Institution, 2015) and a well-graded building sand (4mm

maximum aggregate size) at three water/cement (w/c) ratios (by mass): 0.35, 0.50 and 0.65,

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denoted, respectively, PC35, PC50 and PC65. The mix details of the mortars are presented in

Table 1, with the mean 7- and 28-days compressive strengths (F7 and F28) and the

corresponding bulk conductivities measured at 20oC (7 and 28), obtained from the electrical

measurements detailed below, presented in Table 2. In all mixes, the sand-to-cement ratio

was held constant at 3:1 by weight in accordance with BS EN 196-1 (British Standards

Institution, 2016). To ensure adequate workability for the PC35 mix, a polycarboxylate high-

range water-reducing admixture (BASF MasterGlenium ACE499) was added at 1.25% by

weight of cement.

Fig. 1(a) displays a schematic representation of the mortar sample used within the

experimental programme. To enable impedance measurements, each sample had a pair of

2.4mm-diameter stainless-steel pin electrodes (Grade 316L) spaced at a distance of 10mm

centre-to-centre; at this spacing, the influence of thermal gradients between the electrodes

would be kept to a minimum. During casting and early hardening, the electrodes were held in

position by means of a small acrylic strip located over the centre of the mould. Each pin was

sleeved with heat-shrink tubing apart from the 10mm tip; the tips of the pins were inserted

into the sample to a depth of 30mm. As the electrical field between the tips of the electrodes

was non-uniform, the electrode arrangement had to be calibrated in order to convert electrical

measurements to conductivity and permittivity. This was undertaken using liquids of known

conductivity placed within a cell having identical internal dimensions and electrode

configuration to that of the test samples. Fig. 1(b) displays the calibration curve for the

electrode pair, with measurements undertaken on three electrode pairs. The slope of the

linear-fit curve represents the geometrical constant, evaluated as 46.919 m-1

; in this plot, the

error bars are also included and represent ±1 standard deviation, where error bars appear to be

missing, they are smaller than the data markers. To enable internal temperature monitoring in

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the vicinity of the pins, a thermistor was mounted on the acrylic former at a distance of

<5mm from one of the pins and inserted to a depth of ~20mm (see Fig. 1(a)).

Six mortar samples were cast for each mix using a 2-dm3 Hobart planetary motion mixer:

three were used for impedance tests at 7 days of curing and the remaining three were used for

compressive strength tests at 28-days. A further batch of fifteen samples was cast to monitor

the compressive strength development during the 28-day curing period. After mixing, the

mortar was compacted in two layers, into standard three-gang steel moulds placed on a

vibrating table. They were then covered with polyethylene film to minimize the evaporation

of water. After 24-hr, all samples were demoulded and stored in a curing tank at 20±1oC,

under saturated conditions, until required for testing.

2.2 Electrical measurement and thermal cyclic regime

Electrical impedance measurements were undertaken using an E4980AL high-precision LCR

meter (Keysight, Santa Rosa, US) operating in voltage drive mode at a signal amplitude of

350mV. The LCR meter was controlled by a desktop PC using custom-designed LabVIEW

virtual instrument. Communication with the LCR meter was established across a USB

interface and accessed by the PC using Keysight IO Library Suite software (Version 2017.1).

Prior to testing, one of the mortar samples was removed from the curing tank and surface-

dried with an absorbent towel to negate that any possible surface conduction effects, although

the use of embedded electrodes would already have reduced this influence to a minimum.

The samples were then immediately wrapped with several layers of cling film before being

placed in an environmental chamber to minimise any changes in moisture content during the

entire thermal cycle detailed below. The electrodes embedded in the sample were then

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connected to the voltage high/low and current high/low terminals in the LCR meter via

individually screened short coaxial leads ducted out from the chamber through a small

porthole in the side of the chamber. Changes in internal and chamber temperatures were

monitored using an auto-ranging data logger interfaced to a multiplexing switching unit. In

the present study, the following thermal cycling regime was adopted:

(i) isothermal hold at 20oC for 1-h to allow interior of sample to achieve thermal

equilibrium with the chamber;

(ii) temperature reduction from 20oC to -70

oC at a rate of 10

oC/h;

(iii) isothermal hold for 3-h to allow thermal equilibrium;

(iv) temperature increase to 20oC at the same rate as (ii);

(v) isothermal hold for 3-h to allow thermal equilibrium; and

(vi) (ii)–(v) repeated twice on a 24-h cycle.

Over the entire test regime, both impedance and temperature measurements were recorded

every 2-min, with the impedance measured using the LCR meter over the frequency range

20Hz–1MHz at 20 frequency points per decade. The frequency sweep took ~25s to complete

and the LCR meter was then placed in standby mode until the subsequent measurement was

triggered by the LabVIEW virtual instrument. Thermistor readings from the data logger were

converted to temperature using the Steinhart-Hart equation (McCarter et al., 2012),

[ ] (1)

where is the measured thermistor resistance (Ω); is temperature (in ºC ± 0.2°C); and A,

B, and C are coefficients which depend on the type of the thermistor. In the present study, the

values of A, B, and C were 1.28×10-3

, 2.36×10-4

and 9.31×10-8

K-1

, respectively.

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The time interval between measurements was 2-min and provided virtually continuous

monitoring during the thermal cyclic regime; due to the large amount of data collected only

the impedance and temperature measurements recorded over the first thermal cycle (stages

(ii) to (v)) are presented). It should be noted that although the chamber was taken down to -

70oC, it was only possible to measure the temperature down to approximately -65

oC due to

the resistance of the thermistor reaching the upper limit of the data-logger (1.5MΩ) hence

only data over the temperature range -65oC +20

oC are presented. Fig. 2 displays the

measured chamber (solid line) and internal sample (dashed line) temperatures, which were

converted from thermistor readings using equation (1). It is apparent that the chamber

temperatures during stages (ii) and (iv) exhibit a linear relationship with time at a rate of

10oC/h, highlighting the good performance of the chamber and measurement setup in

delivering the specified rate and range of temperatures.

2.3 Data analysis and presentation

The impedance, , of a cement-based material subjected to a small-signal alternating

current at an angular frequency, , can be expressed in the complex form,

(2)

where and are, respectively, the resistive (real) component and the reactive

(imaginary) component (both in Ω) and √ . These components are normally presented

in Nyquist format and a typical response is displayed schematically in Fig. 3(a). The response

comprises a small spur at the low-frequency end (the right-hand-side) of the plot resulting

from electrode polarisation processes at the electrode-sample interface (which becomes more

defined at lower frequencies), and a semi-circular arc forming over the remainder frequency

range (the left-hand-side) and represents the bulk response. In some cases, the emergence of

an intermediate arc, between the spur and bulk arc, can also be detected and has been

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attributed to either additional polarisation mechanisms within the system itself (McCarter et

al., 2004; Wansom et al., 2006; Suryanto et al., 2016) or additional polarisation mechanisms

at the electrode-sample interface (McCarter et al., 2015b; Suryanto et al., 2018a). These

features are generally modelled by series-connected parallel circuit elements comprising a

resistor, R, and a constant phase element, CPE. The CPE can be described by the frequency

dependent expression,

(3)

where is a constant, √ , and p has a value such that 0<p<1. A CPE with value of

is equal to a pure capacitor with a value of and units in farads (F). When a pure

capacitor is connected in parallel with a resistor, a semi-circular arc is produced (see Fig.

3(a)); however, when a CPE with value of p < 1 is connected, a semi-circular arc whose

centre is depressed under the axis will result and the parameter has now units of Fsp-1

.

The depression angle of the arc, α, can be associated with the exponent, p, through the

relationship,

(4)

2.4 Equivalent circuit modelling

Equivalent circuit analysis was performed using Z-view software Version 3.5b (Scribner

Associates). In the present study, the fitting model comprised two, series-connected parallel

circuits denoted Rb–CPEb to model the bulk arc and Rel–CPEel to account for the electrode

spur (McCarter et al., 2015b). The Rel–CPEel circuit is excluded from the analysis when the

spur is absent in the Nyquist plot. The bulk resistance of the sample, Rb, is obtained at the

projected intercept of the low-frequency end of the bulk arc with the real axis.

3. Test results and discussion

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3.1 Impedance response

Impedance measurements for the three mortar mixes during temperature cycling were found

to extend over three orders of magnitude. Due to the considerable amount of data collected,

only the complex impedance spectra for PC50 mix are presented in Figs. 4(a)-(f) in three

temperature ranges: 20C 0C; -5C -30C; and -35C -65C. In these figures, open

data markers represent the measured response over the frequency range 20Hz–1MHz,

whereas solid lines represent the simulated response; for completeness, the upper frequency

limit of the simulation was extended, passing the peak of the arc, to 30MHz and presented in

dashed lines. In general terms, there is a good agreement between the simulated and

measured responses indicating that the circuit model provides a good representation of the

system. It is evident that as the temperature decreases/increases during the thermal cycle,

there is a progressive displacement of the entire curve to the right (in the case of cooling) and

left (in the case of heating) and results in a gradual enlargement/reduction in the radius of the

bulk arc. This indicates that the two impedance components ( and ) are thermally

activated.

With reference to Figs. 4(a) and (b), it is apparent that the bulk arc over the temperature range

20C 0C only is partially developed due to the upper frequency limit of 1MHz in the

present work. Decreasing the temperature has the effect of increasing the prominence and

definition to the bulk arc i.e. circuit Rb–CPEb and results in an overall increase in impedance,

this effect being due to the reduction in charge mobility with decreasing temperature

(McCarter, 1995; McCarter et al., 2000; Coyle, et al., 2018).

Over the temperature range -5C -30C (Figs. 4(c) and (d)), temperature is seen to have a

similar influence on the overall impedance response to those above freezing/melting

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temperatures, with respect to the displacement and size of the arc on cooling or heating. The

increase in impedance over this temperature range is as a direct result of ice formation in

addition to the effect of decreasing temperature alone. As ice forms within the pore network,

the pore-water volume will decrease (McCarter et al., 2015a; Wang et al., 2016) and this

would have the effect of increasing the overall impedance. Ice formation could also increase

ionic concentration within the unfrozen pore-water which would have an opposing effect

(Sato and Beaudoin, 2011). From Figs. 4(c) and (d), it can be inferred that the increase in

bulk impedance due to ice formation exerts a greater influence than the effect of increasing

ionic concentration. Another interesting feature from Figs. 4(c) and (d) relates to the

difference in the impedance during heating and cooling, with the impedance on heating being

generally greater than that on cooling. This would indicate that a greater volume of ice

remains within the pore system during the melting portion of the cycle than on cooling.

Further studies are being undertaken to obtain the exact interrelationship between volumetric

ice content and conductivity.

The influence of temperature on the displacement and radius of the bulk arc during the

cooling and heating cycles over the temperature range -35ºC -65ºC is still evident (see Figs.

4(e) and (f)) and have similar features to the temperature range -5ºC to -30ºC, with respect to

the displacement and diameter of the arc during the cooling and heating stages. Over this

temperature range, however, there is only minimal difference between the impedance values

on cooling and heating, indicating that there is comparable amount of ice on both portions of

the thermal cycle. It is anticipated that over this temperature range, the free water within the

capillary pores has frozen and conduction would be mainly via the thin lining of pore-water

near to the gel surfaces (McCarter et al., 2015a). The temperature dependence below ~-35ºC

would also reflect the change in the mobility of ions within the pore-water lining.

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Apart from the overall impedance spectra, the temperature influences the frequency values at

salient points on the bulk arc, including the frequency at the cusp-point (i.e. the junction

between the arc and the spur) and the characteristic frequency (i.e. the frequency when the

bulk arc maximizes). When the characteristic frequency could not be evaluated directly from

the test data (i.e. where the bulk arc is only partially developed as is evident in Figs. 4(a) and

(b)), this was determined from the components of the bulk arc circuit used in the simulation

through the relationship (Orazem et al. 2013),

(5)

where and are as per equation (3) and is the bulk resistance (Ω). A summary of

salient frequency values for PC50 mix over the entire temperature range is presented in Table

3 and highlights the temperature dependent nature of these parameters.

3.2 Conductivity and relative permittivity

The impedance of the samples originates from the superposed phenomena of both conduction

and polarization processes operative within the material during thermal cycling. These

quantities are evaluated from the conductivity, , and relative permittivity, (Taha

et al., 2017). The conductivity is a measure of all loss processes operative within the sample

and includes losses due to the motion of free charges under an applied electrical field (i.e.

ionic conduction) and losses due to dissipative polarization processes (Hasted, 1973;

McCarter et al., 1999); the relative permittivity, on the other hand, is a measure of the

polarizability of a material under an alternating electrical field and represents the sum of all

polarisation processes operative at any particular frequency (Suryanto et al., 2016). These

two quantities can be de-embedded from the impedance data and presented in the frequency

domain through the following (Suryanto et al., 2016; 2018b),

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(

) (6)

(

) (7)

where is the permittivity of a vacuum (8.854×10-12

F/m) and k is the geometrical constant

(46.919 m-1

, see Fig. 1(b)).

Figs. 5(a) and (b) display the relative permittivity for PC50 mix during the full thermal cycle

and, for reasons of clarity, is presented in 10oC increments. Considering the plots over the

entire frequency and temperature ranges, they can generally be divided into two distinct

regions:

(i) a region of rapidly decreasing permittivity extending from 20Hz to the cusp-point

frequencies which are indicated in the Figures by solid markers; and,

(ii) a region of slowly decreasing permittivity which extends over the remainder

frequency range up to the upper frequency limit of 1MHz.

Over region (i), the permittivity increases to extremely high values as the frequency decreases

and this can be associated with polarization processes at the electrode/sample interface (Ishai

et al., 2013; McCarter et al., 2015b) and charges on the cement hydrate surfaces which form

electrical double layer (Schwan et al., 1962; Taha et al., 2017), although the latter would

contribute to a much lesser extent. The extent of these polarisation processes over region (i)

decreases with decreasing temperature, particularly at temperatures below the freezing

temperatures. This is evident from Figs. 5(a) and (b); as the permittivity at 20C decreases by

approximately four orders of magnitude over the frequency range 20Hz-1MHz, the

permittivity over region (i) only decreases by approximately one order of magnitude at -40oC.

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The gradual decrease in permittivity over region (ii) can be attributed to the relaxation of both

double-layer polarisation and interfacial (or space charge) polarisation (Hasted, 1973). The

frequency range these polarisations operate is also affected by temperature. At 20oC, it is

proposed that double-layer processes are operative over ~10kHz to ~100kHz, while

interfacial effects will tend to dominant over the remainder frequency range. Below freezing

temperatures, the double-layer effects are seen to dominate at lower frequency values which,

at -40oC, are in the range ~100Hz-1kHz. Superimposed on these polarisation mechanisms are

possible contributions from interfacial relaxation processes resulting from charge separation

at pore-water/ice boundary interfaces. This extends over the remainder frequency range under

consideration.

Figs. 5(c) and (d) display the conductivity at 10oC increments using equation (6) above and

plotted as a function of frequency. The markers correspond to the experimental data while the

lines represent the simulated response which were determined by,

(8)

where represents the ionic conduction effect resulting from the movement of ions through

the interconnected unfrozen pore-water and is the dissipative conduction effect

resulting from relaxation of the polarization processes. The frequency-dependent conductivity

is found to obey the Jonscher equation (Jonscher, 1977),

(9)

where A is a pre-exponential constant and s is the power-law exponent which has a value

such that ; if , then there is no dielectric dispersion and equation (8) will

result in a constant conductivity independent of frequency. It was found that decreases by

approximately three orders of magnitude as the temperature is decreased from 20oC to -60

oC.

was also found to be sensitive to w/c ratio. At 20oC, for example, PC50 at 7- and 28-day

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curing is almost twice as conductive as the PC35 and 20% less conductive than PC65 (see

Table 2). The exponent, , was found to be less sensitive to these factors, generally lying in

the range 0.62-0.66.

With reference to the measured and simulated conductivity plots presented in Figs. 5(c) and

(d), it is apparent that the conductivity increases with frequency and decreases with

temperature. The former is due to additive effect of relaxation of the polarization processes

(i.e. equation (8)), while the latter is due to the reduction in charge mobility with decreasing

temperature and increasing volumetric ice fraction within the pore system (McCarter et al.,

2015a). Three distinctive regions can be delineated from the conductivity plots over the entire

temperature range:

(i) a low-frequency dispersive region of rapidly increasing conductivity resulting from

relaxation of electrode polarisation;

(ii) an intermediate-frequency plateau indicated by a marginal increase in conductivity;

and,

(iii) an extended, high-frequency dispersive region of rapidly increasing conductivity

originating from the dispersion of interfacial polarisation.

The conductivity plots above the freezing temperatures exhibit primarily regions (i) and (ii),

while those below the freezing temperatures exhibit regions (ii) and (iii). This is as a direct

result of frequency shift towards the lower frequencies with decreasing temperature thereby

revealing different portions of the actual spectrum when observed within the same frequency

range.

3.3 Arrhenius relationships and activation energy

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Given that the electrical conduction in the three mixes is primarily ionic in nature, the

conductivity, (S/m), can be related to the sample temperature through an Arrhenius-type

relationship (Chrisp et al., 2001; McCarter et al., 2015a),

(

) (10)

where is the pre-exponential factor which can also be regarded as the nominal conductivity

at infinite temperature; is the activation energy for the conduction process (J/mol); R is the

Universal Gas constant (=8.3141J/mol·K) and T is the absolute temperature (K).

Figs. 6(a), (c) and (e) display the Arrhenius format of the conductivity plots for all mixes over

the temperature range 20oC -65

oC at the projected intercept of the low-frequency end of

the bulk arc with the real axis and at four selected spot frequencies (i.e. 1kHz, 10kHz,

100kHz and 1MHz). The corresponding spot-frequency permittivity plots are presented in

Figs. 6(b), (d) and (f), with the measured and simulated characteristic frequency, fc, values for

the mixes presented in Figs. 8(a)–(c). The measured values represent the observed frequency

values at which the bulk arc maximizes, whereas the simulated values (obtained using

equation (5)) are used when the bulk arc is partially developed, and the peak is absent. The

activation energy for the conduction process, Ea in (kJ/mol), determined from the slope of the

conductivity plots is presented in Figs. 9(a)-(c). In all plots, the solid lines represent the

response during cooling whereas the dashed lines represent the response during heating. In

general, conductivity, permittivity and characteristic frequency plots all display a detectable

frequency and temperature dependency, decreasing with temperature on cooling and

increasing with temperature on heating, highlighting that they all are thermally activated.

With reference to the schematic displayed in Fig. 7, four distinct stages (denoted I–IV) can be

identified on the cooling part of the Arrhenius plots and discussed below together with the

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resulting activation energy; only two stages (essentially stages I, and II-IV combined together)

were present on the heating part.

Stage I: Above freezing temperatures

This stage is characterised by a linear change in conductivity, permittivity and characteristic

frequency with temperature. As the frequency increases, the influence of electrode

polarization, double-layer and interfacial effects decreases and results in an enhancement in

conductivity (Hasted, 1973; McCarter et al., 1999), and a more discernible reduction in

permittivity with increasing frequency. There is only a minor difference in conductivity and

characteristic frequency on cooling and heating, indicating that the bulk response over this

temperature region is dominated solely by temperature and that the conduction is electrolytic

in nature (McCarter et al., 1995). There is a more notable difference in permittivity at the two

lower spot frequencies (i.e. 1kHz and 10kHz) on cooling and heating.

With reference to the activation energy, , presented on Figs. 9(a)-(c), it is apparent that the

value of increases with decreasing w/c ratio and is virtually constant on cooling/heating.

This was evaluated as 23.72/23.07kJ/mol for PC35; 20.10/17.09kJ/mol for PC50; and

19.53/11.88kJ/mol for PC65. As the mobility of ions is controlled by pore size and pore

connectivity, the high in low w/c mix would indicate that the pore network in this mix

must be finer and more disconnected than that in high w/c mix.

The end of stage I is marked by a sudden change in gradient indicating freezing/melting and

the exact occurrence of this feature depends on the w/c ratio and on whether the sample is

either on the cooling or heating portion of the thermal cycle. From Figs. 6(a)-(f), the

temperatures at which freezing/melting takes place are evaluated as -6.40oC/-0.30

oC for PC35,

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-2.19oC/-0.38

oC for PC50 and -1.64

oC/-0.38

oC for PC65. The difference in these salient

temperatures could be explained by the heterogeneous nature of the capillary pore network

which generally considered as comprising large capillary cavities connected by fine pore

necks (i.e. the ink-well model). It has been established that freezing in the cavity is governed

by the radius of pore neck as ice can only propagate into the pore interior/cavity once

freezing has initiated in the pore necks (Schulson et al., 2000; Sun and Scherer, 2010). On

thawing, ice in the pore neck will melt before that in the cavity and as such, melting is

governed by the radius of pore cavity (Schulson et al., 2000; Swainson and Schulson, 2001).

Accordingly, the temperature at which freezing/melting occurs could give an estimate of the

mean radii of the pore-neck and pore-cavity which could be approximated using the Gibbs–

Thomson equations (Brun et al., 1977; Sun and Scherer, 2010; McCarter et al., 2015a),

(11a)

(11b)

where and are, respectively, the depression in the freezing-point and melting-point

with respect to the normal freezing/melting point of ice (assumed as 0oC). These equations

also take into account the thickness of unfrozen pore-water lining (=0.8nm) (Schulson et al.,

2000; Sun and Scherer, 2010). Equation 11(a) was proposed based on the assumption that

when ice forms within the pore network, the interface between the ice and water takes a

spherical shape, while in equation 11(b) ice melting is assumed to start from a cylindrical-

shape pore wall. Based on these equations, the computed radii of the pore-neck and pore-

cavity are summarized in Table 4, showing clearly the influence of w/c ratio on pore

dimensions. Furthermore, given that the radius of pore entry has a governing role on freezing

and the maximum radius of pore cavity has a defining role on melting, this difference causes

a hysteresis to develop and is discussed below.

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Stage II: Ice formation and melting within the capillary pores

Within this region, the conductivity, permittivity and characteristic frequency continue to

decrease. With reference to Figs. 6(a)-(f), on freezing, this region generally starts with a

nonlinear response and continues with a quasi-linear response to approximately -40oC, with

the exception of PC35 which displays a nonlinear response throughout. Over the initial

portion of the stage, both PC50 and PC65 exhibit an abrupt change in slope (see Figs. 6(c)-(f))

resulting in an anomalously high value of (see Figs. 9(b) and (c)), the extent of which

increases with increasing w/c. The transitory increase in would signify that additional

energy is required for the liquid/solid (and solid/liquid) phase change (Farnam et al., 2015;

Tomlinson et al., 2017) while the sudden change in magnitude would reflect instantaneous

ice formation (or melting) in the capillary pore network. Following this peak, it is apparent

from Figs. 9(a)-(c) that decreases abruptly with temperature and eventually achieves an

almost constant value as the process of accretion and infilling of the pore network with ice

slows down. This process starts from approximately -10oC which also marks the beginning of

the linear part in the Arrhenius plots displayed in Figs. 6(a), (c) and (e).

During this linear portion, it is apparent that the value of is generally much higher than

that during stage I, highlighting the additional influence of ice formation than just

temperature alone. At this stage, would reflect the energy required for ionic movement

within the thin lining of pore-water near to the gel surfaces which, during the cooling/heating

portion of the thermal cycle (see Figs. 9(a)-(c)), is evaluated as 41.1/45.9kJ/mol for PC35;

48.8/52.3kJ/mol for PC50; and 55.4/53.6kJ/mol for PC65. Moreover, it is of interest to note

that on cooling, there is another, relatively weak peak at approximately -25oC, possibly

resulting from ice nucleation inside smaller interconnected capillary pores (or open gel pores)

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(Bager and Sellevold, 1986; Bentz, 2006; De Fontenay and Sellevold, 1980). This feature is

not detected on thawing.

Another important feature from Figs. 6(a), (c) and (e) relates to the value of the conductivity,

with the conductivity on cooling being consistently higher than that on heating resulting in

the development of hysteresis in the thermal cycle. As before, this is due to the ink-well effect,

with the pore neck controlling ice formation/thawing in the pore cavity. The lower

conductivity on thawing would indicate that a greater volume of ice remains within the pore

system than on freezing. Aside from hysteresis, it is apparent from Figs. 6(a), (c) and (e) that

the measurement frequency has a significant influence on stage (II) than stage (I), particularly

over the initial region of stage (II) from which an increasing trend of conductivity with

increasing frequency is evident. This is attributed to a combined influence of the dissipative

conduction effect associated with relaxation of the polarisation (i.e. double-layer and

interfacial) processes and the frequency shift towards the lower frequencies with decreasing

temperature (see, for example, the trend in characteristic frequency with temperature in Figs.

8(a)-(c)). It is interesting to note from Figs. 6(a), (c) and (e) that, while the extent of

relaxation during stage (I) is greater than that during stage (II) (see Figs. 6(b), (d) and (f)), the

dissipative conduction effect in stage (II) exerts a greater influence on conductivity than

during stage (I), signifying a greater contribution of this part to the overall conduction.

Stage III: Ice formation within the gel pores

This stage is characterised by nonlinear Arrhenius responses as shown in Figs. 6(a)-(f) and

Figs. 8(a)-(c), and a notable increase in in Figs. 9(a)-(c), resulting from a phase change. As

ice formation is controlled by the diameter of the pore-neck, ice nucleation at this

temperature range should have occurred in a much finer pore network (viz, gel pores)

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(Johannesson, 2010; Kjeldsen and Geiker, 2008; San et al., 2011; Scherer, 1993; Synder and

Bentz, 2004). It is interesting to note from Figs. 9(a)-(c) that regardless the w/c ratio,

appears to increase from ~ -38oC and reaches its peak at ~ -42

oC before gradually decreasing

and becoming constant despite being masked by the variation in measured values.

With reference to all conductivity, permittivity and characteristic frequency plots, it is evident

that at the start of stage III, as before, the conductivity on cooling is consistently higher than

that on heating indicating that there is more ice in the gel pore network on heating than on

cooling. The difference diminishes with decreasing temperature and the temperature at which

the two plots merge is affected by w/c ratio, decreasing from -47.36oC for PC65 to -50.56

oC

for PC50 and -54.10oC for PC35. This variation would indicate that although ice nucleation

in the gel pores starts from approximately the same temperature (approximately -40oC) which

indicates comparable maximum size of gel pores, PC35 has finer pores and a broader gel-

pore size distribution.

Stage IV: Ice saturation

Within this stage, temperature and frequency are again seen to have a dominant influence,

with all conductivity and characteristic frequency plots displaying an almost linear

relationship with temperature, decreasing/increasing with decreasing/increasing temperature

(respectively). While the permittivity displays a similar trend, it exhibits a gradual decrease in

value with temperature, reaching almost a constant value at the low temperature end (~100 at

1kHz and decreasing to ~20 at 1MHz). This low permittivity at high frequency would

indicate that the pore space has been saturated by ice and that the ice content would be

virtually constant (De Fontenay and Sellevold, 1980). Moreover, it is intetesting to note that

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over this temperature range, there are no more hysteresis effects in all plots implying that the

volumetric ice content on cooling is comparable to that on heating.

With reference to Figs. 6(a), (c) and (e), it is of interest to note that the dissipative conduction

effect has a greater contribution to the overall conduction with increasing frequency than the

previous two stages despite the extent of relaxation with decreasing temperature becoming

less prominent (see Figs. 6(b), (d) and (f)). This would reflect the decreasing contribution of

the ionic conduction effect and increasing contribution of the dissipative conduction effect

with decreasing temperature.

4. CONCLUSIONS

The electrical impedance and thermal responses of cement mortars with varying w/c ratios

were investigated over the frequency range 20Hz-1MHz and the temperature range

+20 -70oC. Measured data are presented in four formats: Nyquist, frequency domain,

Arrhenius and activation energy to provide a comprehensive picture of the nature of

conduction and polarisation processes operative within the materials over a wide frequency

and temperature range. The following conclusions can be drawn from the work presented:

(1) Electrical conduction in cement matrix over the extended temperature range is shown to

display a natural temperature and frequency dependence. Polarisation processes

operative within the cement matrices are also shown to be thermally activated.

(2) The conduction above freezing temperatures depends on the size and connectivity of

capillary pore network, with the conductivity generally decreasing with w/c ratio and

temperature and increasing with increasing frequency due to relaxation of polarisation

processes. Below freezing temperatures, it is shown that electrical conduction is also

influenced by the volumetric ice content. The dissipative conduction effect resulting

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from relaxation of polarisation processes was found to exert a greater influence on the

overall conduction with increasing frequency and decreasing temperature.

(3) Between the freezing points and approximately -50ºC, the conductivity and permittivity

on cooling are generally higher than that on heating, suggesting the presence of a

greater volume of ice within the pore network on thawing, which results in hysteresis in

the cooling/heating cycle. At lower temperatures, there is no detectable difference in

conductivity and permittivity on freezing and thawing and attributed to no further ice

formation.

(4) When presented in an Arrhenius format, four distinct regions could be identified on the

cooling part of both conductivity and permittivity measurements and results are

explained in terms of temperature effects, ice formation within the capillary and gel

pore network, and relaxation of polarisation processes. In contrast, only two regions

could be delineated on the heating part of the thermal cycle.

(5) The activation energy at above freezing temperatures increases with decreasing w/c

ratio, whereas a reverse trend is found below the freezing temperatures.

(6) Three well defined peaks are evident from the activation energy plots on freezing. The

first peak is related to the pore-neck radii of capillary pores, the second to the radii of

fine capillary pores and the third to the radii of gel pores. Only one peak is detected on

thawing and this can be related to the radii of pore cavities. Work is now continuing to

obtain the pore size distribution.

Finally, it is worth noting that the testing procedure presented in this paper is technically

simple to perform and could be equally applied to concretes. It is anticipated that although

concretes would display considerably lower conductivity values, due to the diluting effects of

the aggregate, they would display comparable response as conduction and polarisation

process would occur in the cementitious binder. Work is continuing in this respect.

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Acknowledgements

The Authors wish to acknowledge the financial support of the Engineering and Physical

Sciences Research Council, United Kingdom (Grant EP/N028597/1). They also wish to thank

Professor Malcolm Chrisp (Head of School) for placing the facilities of the School at their

disposal.

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Technol. 151, 314–322. https://doi.org/10.1016/j.coldregions.2018.03.027

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Figure captions

Fig. 1 (a) Schematic of mortar sample and (b) geometrical parameter for the electrode

configuration used in this study.

Fig. 2 Variation in temperature of chamber and internal temperature of sample during one

freeze/thaw cycle.

Fig. 3 (a) Schematic diagram of Nyquist plot in a cement-based system and (b) equivalent

electrical circuit.

Fig. 4 Nyquist plots for PC50 mortar sample between 20ºC to -65ºC, with freezing response

presented in the left and melting in the right. Measured values are presented in open marks,

characteristic values in closed marks and simulated response in lines.

Fig. 5 (a)-(b) Relative permittivity and (c)-(d) conductivity for PC50 mortar sample.

Fig. 6 Arrhenius plots for all mixes: (a), (c) and (e) conductivity and (b), (d) and (f) relative

permittivity.

Fig. 7 Schematic diagram indicating four stages in the Arrhenius plots during cooling.

Fig. 8 Measured and computed characteristic frequency values for all mixes presented in the

Arrhenius format.

Fig. 9 Arrhenius plots of the activation energy for electrical conduction processes over the

thermal cycling regime for all mixes.

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(a)

50

50

10

30

Thermistor

Heat shrink

sleeving

10

0 5 10 15 20 25

0

2

4

6

8

10

12

= 46.919/R

r2 =0.99

(

10

-2 S

/m)

1/R (10-4 S)

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(b)

Fig. 1.

Fig. 2

(a)

0 4 8 12 16 20 24

-80

-60

-40

-20

0

20

Tem

per

ature

(C

)

Time (hr)

Chamber

PC35

PC50

PC65

Cooling

Heating

1

10

1

10

R

C

Depressed arc

ElectrodeBulk

Increasing

frequency

aZ'(w)

-iZ

''(w

)

2pfc

Rb

CPE

R

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(b)

Fig. 3

Rb

CPEb CPEel

Rel

Bulk Electrode

0.0 0.5 1.0 1.5 2.0 2.5 3.0

-1.5

-1.0

-0.5

0.0

(a) 20C 0C

Z'(kW)

20 15

10 5

0

Z''

(kW

)

Cooling

0 10 20 30 40 50 60

-30

-20

-10

0

Z'(kW)

-5 -10

-15 -20

-25 -30

Z''

(kW

)

(c) -5C -30C

20Hz

1MHz

0 1 2 3 4 5

-2

-1

0

0.20

-0.1

0

(e) -35C -65C

Z'(MW)

-35 -40

-45 -50

-55 -60

-65

Z''

(MW

)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

-1.5

-1.0

-0.5

0.0

(b) 20C 0C

Z'(kW)

20 15

10 5

0

Z''

(kW

)

Heating

0 10 20 30 40 50 60

-30

-20

-10

0

(d) -5C -30C -5 -10

-15 -20

-25 -30

Z''

(kW

)

Z'(kW)

1MHz

20Hz

0 1 2 3 4 5

-2

-1

0

0.20

-0.1

0

Z'(MW)

-35 -40

-45 -50

-55 -60

-65

Z''

(MW

)

(f) -35C -65C

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Fig. 4

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101 102 103 104 105 106

101

102

103

104

105

106

107

108

Cooling

(a)

e r

Frequency (Hz)

20

10

0

-10

-20

-30

-40

-50

-60

101 102 103 104 105 106

101

102

103

104

105

106

107

108

Heating

e r

Frequency (Hz)

20

10

0

-10

-20

-30

-40

-50

-60

(b)

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Fig. 5

101 102 103 104 105 106

10-6

10-5

10-4

10-3

10-2

10-1

100

Cooling

(

S/m

)

Frequency (Hz)

-20 10 0 -10 -20

-30 -40 -50 -60

(c)

101 102 103 104 105 106

10-6

10-5

10-4

10-3

10-2

10-1

100

Heating

(

S/m

)

Frequency (Hz)

-20 10 0 -10 -20

-30 -40 -50 -60

(d)

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3.3 3.6 3.9 4.2 4.5 4.8

-12

-10

-8

-6

-4

-2

Cusp

1kHz

10kHz

100kHz

1MHz

Increasing

frequency

Ln (

)

(S/m

)

1000/T (K-1)

(a) PC35

Increasing

frequency

0oC

Cooling

Heating

3.6 3.7 3.8-5.0

-4.5

-4.0

3.3 3.6 3.9 4.2 4.5 4.8

2

4

6

8

10

12

1kHz

100kHz

10kHz

Ln (

e r)

1000/T (K-1)

1MHz

(b) PC35

Increasing

frequency

Cooling

Heating

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3.3 3.6 3.9 4.2 4.5 4.8

-12

-10

-8

-6

-4

-2

frequency

Cusp

1kHz

10kHz

100kHz

1MHz

Ln (

)

(S/m

)

1000/T (K-1)

(c) PC50

Increasing

frequency

0oC

Increasing

Cooling

Heating

3.6 3.7 3.8-4.5

-4.0

-3.5

-3.0

3.3 3.6 3.9 4.2 4.5 4.8

2

4

6

8

10

12

Ln (

e r)

1000/T (K-1)

(d) PC50

1kHz

10kHz

100kHz

1MHz

Increasing

frequency

Cooling

Heating

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Fig. 6

3.3 3.6 3.9 4.2 4.5 4.8

-12

-10

-8

-6

-4

-2

Cusp

1kHz

10kHz

100kHz

1MHz

Ln(

) (S

/m)

1000/T (K-1)

(e) PC65

0oC

Heating

Cooling

Increasing

frequencyIncreasingfrequency

3.6 3.7 3.8-4.5

-4.0

-3.5

-3.0

3.3 3.6 3.9 4.2 4.5 4.8

2

4

6

8

10

12

Ln (

e r)

1000/T (K-1)

Cooling

Heating

(f) PC65

1kHz

10kHz

100kHz

1MHz

Increasing

frequency

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Fig. 7

3.3 3.6 3.9 4.2 4.5 4.8

Ln (

)

(S/m

)

1000/T (K-1)

the interconnected capillary pore network

Freezing starts inside

the gel pore networkFreezing starts inside

er

I II III IV

end point

Melting

3.3 3.6 3.9 4.2 4.5 4.8

Ln (

e r)

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3.3 3.6 3.9 4.2 4.5 4.8

6

8

10

12

14

16

18

Simulated values

Cooling

Heating

Ln

(f c

) (H

z)

1000/T (K-1)

(a) PC35

Measured values

Cooling

Heating

3.3 3.6 3.9 4.2 4.5 4.8

6

8

10

12

14

16

18

(b) PC50 Cooling

Heating

Ln

(f c

) (H

z)

1000/T (K-1)

Cooling

Heating

Measured valuesSimulated values

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Fig. 8

3.3 3.6 3.9 4.2 4.5 4.8

6

8

10

12

14

16

18

(c) PC65

Cooling

Cooling

Heating

Ln

(f c

) (H

z)

1000/T (K-1)

Heating

Measured valuesSimulated values

3.3 3.6 3.9 4.2 4.5 4.8

0

50

100

150

200

-6.5C-3C-24C

Heating

Ea

(kJ/

mo

l)

1000/T (K-1)

Cooling

Heating(a) PC35

Cooling

-42C

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Fig. 9

3.3 3.6 3.9 4.2 4.5 4.8

0

50

100

150

200

Ea

(kJ/

mo

l)

1000/T (K-1)

Cooling

Heating(b) PC50

Cooling

Heating

-43C

-25C

-2C

-0.5C

3.3 3.6 3.9 4.2 4.5 4.8

0

50

100

150

200

Ea

(kJ/

mo

l)

1000/T (K-1)

Cooling

Heating

Heating

(c) PC65

Cooling

-41C

-24C

Freezing: -1C

Melting: -0.5C

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Table captions

Table 1. Summary of mortar mixes (w/c = water/cement ratio; Pl = plasticiser; F28 = 28-day

compressive strength).

Table 2. Compressive strength and bulk conductivity at 7- and 28-days of curing

(F = compressive strength determined at age indicated; σ = bulk conductivity at 20oC).

Table 3. Salient frequencies on Nyquist plot for PC50 mix.

Table 4. Estimated pore-neck (rpn1 and rpn2) and pore-cavity (rpc) radii.

Table 1. Summary of mortar mixes (w/c = water/cement ratio; Pl = plasticiser).

Mix designation w/c CEM I

(kg/m3)

Fine

(kg/m3)

Pl

(kg/m3)

PC35 0.35 555 1665 6.94

PC50 0.50 512 1537

PC65 0.65 476 1428

Table 2. Compressive strength and bulk conductivity at 7- and 28-days of curing

(F = compressive strength at age indicated; σ = bulk conductivity at 20oC).

Mix designation F7

(MPa)

σ7

(S/m)

F28

(MPa)

σ28

(S/m)

PC35 71.8 0.029 83.5 0.025

PC50 46.9 0.050 64.0 0.046

PC65 25.6 0.063 43.4 0.059

Table 3. Salient frequencies on Nyquist plot for PC50 mix (+ not determined).

Temperature

(ºC)

Freezing cycle Thawing cycle

Characteristic

frequency (Hz)

Cusp-point

frequency (Hz)

Characteristic

frequency(Hz)

Cusp-point

frequency

(Hz)

20 15.7×106#

12.6×103 15.7×10

6# 12.6×10

3

10 9.9×106#

10.0×103 11.5×10

6# 12.6×10

3

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0 6.2×106#

7.1×103 7.3×10

6# 10.0×10

3

-10 2.1×106#

2.8×103 1.6×10

6# 1.8×10

3

-20 8.4×105 1.4×10

3 6.2×10

5 5.0×10

2

-30 3.2×105 3.6×10

2 2.5×10

5 89

-40 1.1×105 + 89.1×10

3 +

-50 2.8×104 + 2.8×10

4 +

-60 7.1×103 + 7.1×10

3 +

# Values derived from simulated response.

Table 4. Estimated pore-neck (rpn1 and rpn2) and pore-cavity (rpc) radii.

Mix Temperature (ºC) Estimated pore radius (nm)

ΔTf1 ΔTf2 ΔTt

Equation 11a Equation

11b

rpn1 rpn2 rpc

PC35 -6.5 -42.0 -3.0 10.5 2.11 11.5

PC50 -2.0 -43.0 -0.5 32.9 2.07 65.3

PC65 -1.0 -41.0 -0.5 65.2 2.15 65.3

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Highlights

- Electrical properties of Portland cement mortars under freezing/thawing evaluated

over the bandwidth 20Hz–1MHz.

- Influence of temperature and ice formation on conduction and polarization

processes highlighted.

- Hysteresis effects present over a significant portion of the freezing/thawing cycle.

- Freezing and melting point depressions allowed the estimation of the radius of the

pore-neck and pore-cavity.

- Dissipative conduction effect resulting from the relaxation of polarisation processes

becoming more discernible with decreasing temperature.

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