Can Moisture Buffer Performance be Estimated from Sorption Kinetics?

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knowledge of the moisture buffer performance of the materials inside it, guidelines ... of commonly used rendering materials in moisture sorption kinetics is a step.
Can Moisture Buffer Performance be Estimated from Sorption Kinetics? J. M. P. Q. DELGADO, N. M. M. RAMOS AND V. P. DE FREITAS* LFC – Laborato´rio de Fı´sica das Construc¸o˜es Departamento de Engenharia Civil Faculdade de Engenharia da Universidade do Porto Rua Dr Roberto Frias, s/n 4200-465 Porto, Portugal (Received July 13, 2005)

ABSTRACT: This article describes the research on the moisture buffering effect of building materials. A set of experiments on samples of current building materials are conducted under transient conditions of relative humidity (RH). The results obtained are then analyzed using kinetics models. The experimental settings are based on the moisture buffer value (MBV) test method currently under study by Nordic researchers. The main result from these tests is the MBV number that can be used to characterize the moisture buffer performance of a material or a system. The application of kinetics models to the experimental results is explored and several parameters are retrieved. A proposal for the use of these parameters is presented and its practical use is discussed. KEY WORDS: kinetics models, sorption curves, moisture buffer value, building materials.

INTRODUCTION inside a dwelling plays an important role in the user’s satisfaction, not only due to its influence on comfort, but also when high values are persistent, surface condensation may take place in large proportions, being a problem for the users and bringing about economic and social consequences. In our opinion the moisture buffer performance of the walls and ceiling covering materials, as well as furniture and textiles inside the buildings, condition their hygroscopic inertia, which can have an important role in the reduction of high humidity peaks.

T

HE RELATIVE HUMIDITY (RH)

*Author to whom correspondence should be addressed. E-mail: [email protected]

Journal of BUILDING PHYSICS, Vol. 29, No. 4—April 2006 1744-2591/06/04 0281–19 $10.00/0 DOI: 10.1177/1744259106062568 ß 2006 SAGE Publications

281

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J. M. P. Q. DELGADO

ET AL.

If the prediction of a room’s hygroscopic inertia could be related to the knowledge of the moisture buffer performance of the materials inside it, guidelines for building designers could be proposed. The work of several researchers (Ojanen and Salonvaara, 2003; Mitamura et al., 2001; Padfield, 1998) has already demonstrated the benefits of inside RH variation control provided by hygroscopic materials. We believe that the characterization of commonly used rendering materials in moisture sorption kinetics is a step in the right direction to define their contribution to the hygroscopic inertia of a room. In this article, we propose a way of exploring the dynamic behavior of building materials with a set of kinetics parameters, as defined in the ‘Theory’ section, which can be derived from experiments. Three quantities are obtained from the test: (i) the change in mass under a given RH, (ii) the time required for that change to occur, and (iii) the rate of change of mass with time. The experimental settings were defined regarding the usual operation conditions inside buildings. The RH ranges adopted on the tests fall on the interval 33–85% which includes most of the values usually measured in real situations. Although the upper value is a bit high, as 75% would be the obvious upper limit, it was chosen to explore the less linearity of materials behavior under higher RH ranges. The specific conditions of Portuguese climate during winter, with high outdoor RH and outdoor temperatures often above 10 C added to the traditional poor heating, also justifies the option for high RH ranges in the tests. In this initial work, materials that can be used close to the inside air were tested but the influence of finish coatings and temperature variation on kinetics parameters was not explored. THEORY The curvature of sorption will vary from material to material, but the vast majority of building materials follow a general curvature shape similar to Type I adsorption isotherm which are well represented by the Langmuir isotherm (Langmuir, 1918). Various kinetics models have been suggested for adsorption processes under static conditions. In order to investigate the mechanism of sorption in building materials, some adsorption models were used to test dynamical experimental data. Lagergren (1898) suggested the first-order rate equation,   dw ¼ K1 weq  w dt

ð1Þ

Estimation of Moisture Buffer Performance

283

Integrating this equation for the initial and end conditions t ¼ 0 to t ¼ t and w ¼ 0 to w ¼ w, Equation (1) may be rearranged for linearized data plotting as shown by Equation (2):     K1 t log weq  w ¼ log weq  2:303

ð2Þ

and for desorption the boundary conditions t ¼ 0 to t ¼ t and w ¼ wi to w ¼ w gives   w ¼ weq þ wi  weq expðD1 tÞ

ð3Þ

where w and weq are the water content at any time and at equilibrium, respectively, and K1 and D1 are the rate constant of first-order adsorption and desorption, respectively. In order to fit Equation (2) to experimental data, the equilibrium sorption capacity, weq, should be known. In most cases from the literature, the pseudo-first-order equation of Lagergren does not fit well over the range of contact times under investigation. Furthermore, one has to find some means of extrapolating the experimental data to t ! 1, or treat weq as an adjustable parameter to be determined by trial and error. For this reason, it is necessary to use a trial and error solution method to obtain the equilibrium sorption capacity, weq. Another model for the analysis of sorption kinetics is the pseudo-secondorder model developed by Ho and McKay (1999). The rate law for this system is expressed as  2 @w ¼ K2 weq  w @t

ð4Þ

Integrating Equation (4), for the boundary conditions t ¼ 0 to t ¼ t and w ¼ 0 to w ¼ w gives 1 1 ¼ þ K2 t weq  w weq

ð5Þ

and for desorption process, with the boundary conditions t ¼ 0 to t ¼ t and w ¼ wi to w ¼ w, gives 1 1 ¼ þ D2 t weq  w weq  wi

ð6Þ

284

ET AL.

t/w

J. M. P. Q. DELGADO

b

q

t Figure 1. Dependence of t=w ¼ fðtÞ for the kinetics model of sorption.

where K2 and D2 are the pseudo-second-order rate constant of sorption and desorption, respectively. Equation (5), can be rearranged to obtain a linear form, t ¼ at þ b w

ð7Þ

with a ¼ 1/weq (slope) and b ¼ 1=K2 w2eq (intercept). The plot of t/w versus t gives a straight line (Figure 1) and the equilibrium water content and sorption rate constant could be evaluated from the slope (weq ¼ tan1 ) and intercept, respectively. However, there are some building materials whose mass variation in function of time is not well represented by the solution of first or secondorder sorption kinetics equations. In these situations, it is necessary to use the general form of Equation (1):  n dw ¼ Kn weq  w dt

ð8Þ

and the integration of Equation (8) with the same boundary conditions of Equation (1) gives: 1 1 þ Kn t  n1 ¼ n1 ðn  1Þw ðn  1Þ weq  w eq the general solution of Equation (8), valid for n>1.

ð9Þ

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Estimation of Moisture Buffer Performance

Interesting parameters obtained by sorption kinetic equations are the initial sorption rate, h, and the time to reach 50% of equilibrium water content, t0.5, given by  h¼ t0:5 ¼

 dw ¼ Kn wneq dt t¼0

2n1  1 ðn  1ÞKn wn1 eq

ðvalid for n > 1Þ

ð10Þ ð11Þ

Extrapolation of Sorption Kinetic Curves This method was developed by Ja¨ntti et al. (1970) for simple adsorption processes and was used for fast calculation of adsorption data, by measuring of some values of adsorption water content at short time intervals at the beginning of the sorption kinetic curve and extrapolation of the equilibrium water content. With this method the adsorbed mass is measured at three different times (where t ¼ t2  t1 ¼ t3  t2 ) yielding the values w1, w2, and w3, respectively. For the evaluation involved Ja¨ntti offered the choice between three molecular adsorption mechanisms represented by the following equations:   wðtÞ ¼ weq 1  et= t= 1 þ t= t wðtÞ ¼ weq tanh 

wðtÞ ¼ weq

ð12Þ ð13Þ ð14Þ

where Equation (13) is the Langmuir adsorption model (very similar to pseudo-second-order model). The variable w(t) is the momentary adsorption at time t,  is the so-called characteristic time, weq is the adsorbed mass after waiting infinitely long, hence it is the quantity, determination of which is the aim of the measurement. For the calculation of the adsorption weq Ja¨ntti et al. used the equations, respectively: weq ðt2 Þ ¼

wðt2 Þ2 wðt1 Þwðt3 Þ 2wðt2 Þ  wðt1 Þ  wðt3 Þ

ð15Þ

weq ðt2 Þ ¼

wðt1 Þwðt2 Þ þ wðt2 Þwðt3 Þ  2wðt1 Þwðt3 Þ 2wðt2 Þ  wðt1 Þ  wðt3 Þ

ð16Þ

286

J. M. P. Q. DELGADO

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi wðt1 Þwðt2 Þ2 þwðt2 Þ2 wðt3 Þ  2wðt1 Þwðt2 Þwðt3 Þ weq ðt2 Þ ¼ 2wðt2 Þ  wðt1 Þ  wðt3 Þ

ET AL.

ð17Þ

The authors used this method for adsorptions satisfying Equations (12)–(14) where the weq ðt2 Þ function, calculated from the measured values of w, is independent of t and equal to weq, what leads to a knowledge of this value very soon after the beginning of the measurements. The parameter  is calculated for infinitesimally small values of t, using the equation: ¼

weq ðt2 Þ  wðt1 Þ ðt2  t1 Þ wðt2 Þ  wðt1 Þ

ð18Þ

EXPERIMENTS The assessment of building materials’ moisture buffer capacity is essential for predicting the potential impact of those materials on the RH control inside a room. The recent work of several researchers (Padfield, 1998; Reick and Setzer 1998; Mitamura et al. 2001; Ojanen and Salonvaara, 2003) and the conclusions from the NORDTEST Workshop on Moisture Buffer Capacity (Rode et al. 2003; Rode et al. 2004), inspired the specific tests that are presented in this article. The results of these experiments enable to characterize the kinetics of mass exchange between air and materials and also provide a way of comparing different materials in terms of their contribution to the room’s hygroscopic inertia. In these tests, several specimens of building materials are submitted to transient conditions of RH. These experiments simulate the cyclic variations in moisture loads and RH levels that can be found in bedrooms, for instance, where during the night, there will be an increase in RH due to vapor production by the occupants. To perform these experiments, a climatic chamber was used (Figure 2) to subject the specimens to simulated climatic conditions over extended periods of time; namely the control of temperature and RH. Both the RH and the temperature of the chamber can be independently controlled to constant values or to cycles of change. The transition from low to high RH values inside the chamber can be achieved after 30 min and the opposite movement will be attained in 1 h. A precision balance was located inside the climatic chamber and the mass change registered continuously by a personal computer.

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Estimation of Moisture Buffer Performance Input signal

Output signal Dw (g/m2)

RH (%)

t (s) Change of RH

t (s) Change of mass/area

Specimen

Climatic chamber

Precision balance

Personal computer (data logger)

Figure 2. Sketch of experimental set-up.

Materials Analyzed In these experiments, an option was made in using specimens of common materials used in Portugal as coverings in walls and ceilings. The experiments were performed with gypsum plasterboard, gypsum plaster and cement plaster specimens; and with a vitrified back and sealed around the edges, leaving only one open surface. Another specimen used was plywood, sealed with aluminum foil around the edges, leaving only two open surfaces. Each specimen was tested for a period of few days with a square wave of RH, with 12-h steps, and a constant temperature of 20 C. The high value used for RH was 85% in most of the experiments. The gypsum plaster and cement plaster specimens were also subjected to a set of cycles of the same type but where the high RH was only 75%. The experiments with plywood samples were performed with a square wave of RH with step cycles of 8 h with 75% RH followed by 16 h at 33% RH, and a constant temperature, 23 C. The tests were run until the cyclic behavior of the specimen was stable, that is, when the cycles fully repeated themselves (Table 1). With the objective to know the water vapor mass gain for the RH step studied, the building materials used in our experiments were stabilized (until no change in weight was observed) in a climatic chamber at 65% or 33% of RH. Afterwards, the specimens used were placed in a climate box immediately after weighing, on a balance with a resolution of 1 mg. A climate box was used for conditioning the specimens. The box was placed in a room with controlled temperature and a saturated salt solution was

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ET AL.

Table 1. Materials used in our experiments.

Materials Gypsum plasterboard Gypsum plaster Gypsum plaster Plywood Cement plaster Cement plaster

T ( C)

 (kg/m3)

A (m2)

Thickness (mm)

RH (%)

Cycles (h)

20 20 20 23 20 20

750 1340 1340 430 1950 1950

0.2  0.2 0.2  0.2 0.2  0.2 2(0.2  0.2) 0.2  0.2 0.2  0.2

14 8 8 10 15 15

65–85 65–85 65–75 33–75 65–85 65–75

12–12 12–12 12–12 8–16 12–12 12–12

used to obtain the desired RH in the climate box. The RH (generated by the salt solution) was 85  0.4% (KCl) or 75  0.3% (NaCl), Greenspan (1977), and the specimens were left in the boxes until no change in weight was observed. RESULTS The series of tests performed on the specimens meant to analyze the response in terms of water content variation. These tests followed closely the conclusions from the NORDTEST workshop on moisture buffer capacity and its proposed definition of moisture buffer value (MBV) as a single number derived from these experiments. MBV Analysis Figure 3 shows the mass variation observed in six different tests, during the experiments. The main result of each test is presented in a single number format, defined as MBV, which represents the peak-to-peak difference, of the stable cycle, in specimen weight of moisture uptake per open surface area and per % RH variation (Table 2). Sorption Kinetics Analysis As an additional way of characterizing the materials’ hygroscopic capacity leads us to the application of the presented kinetics models to the results of these tests. We analyzed the experimental results for the sorption phase of the initial cycle and the stable cycle. Based on the performed analysis, it was found that the sorption of water vapor onto these building materials proceeds in accordance with the pseudo-second-order model, except for cement plaster. This is confirmed by rectilinear diagrams of sorption showed in Figure 4(a) and (b).

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Estimation of Moisture Buffer Performance 70

Gypsum plaster board (65-85%, 20°C) Gypsum plaster (65-85%, 20°C) Gypsum plaster(65-75%, 20°C) Cement plaster (65-85%, 20°C) Cement plaster (65-75%, 20°C) Plywood (33-75%, 23°C)

60

∆w/A (g/m2)

50 40 30 20 10 0 0

20

40

60

80 t (h)

100

120

140

160

Figure 3. Experimental mass variation of different building materials.

The experimental values do not deviate from the lines by more than 12% and the correlation coefficients were 0.99. The kinetics parameters of the water vapor sorption on building materials tested are listed in Table 2, including the experimentally found half-time, equilibrium water content and theoretical kinetic parameters calculated from Equations (7), (10), and (11). Examples of experimental curves, obtained from experimental data, of sorption are shown in Figure 5(a) and (b). This analysis was used on cement plaster specimen, but the curves were not well represented by the solution of pseudo-second-order sorption kinetics equation. Hence, we decided to use Equation (9), and the best fitted solution for cement specimens was obtained with n ¼ 5 (Figure 6), for initial and stable cycle. Studies conducted by Johannesson (2002) found a pseudo-fourth-order sorption kinetics behavior for mature cement mortar. This result may be explained by the fact that cement mortar, due to the continuous processes of hydration, does not have a stable pore structure. Effect of Different Relative Humidity Amplitude Figures 4(b), 7(a) and (b) show two different amplitudes of RH variation that were applied to gypsum plaster and cement plaster specimens, at the initial and stable cycle. The results from the MBV show that the behavior of the specimen could be extrapolated from one test to the other, using a scale factor proportional to the RH difference, to multiply the set of values of one

290

Table 2. Kinetic parameters obtained by sorption kinetic equations; at initial(1) and stable cycles(2). weq (g/m2)

K2  103 (m2/kg s)

t0.5 (h)

1.25

36.1 32.5

1.86 2.29

4.14 3.74

Gypsum plaster (65–85% RH)

1.13

45.8 40.0

1.44 1.51

Gypsum plaster (65–75% RH)

1.30

20.3 19.5

Plywood (33–75% RH)

0.73

Cement plaster (65–85% RH) Cement plaster (65–75% RH)

Gypsum plasterboard (65–85% RH)

(1)

n1 K ¼ Kn w eq (h1)

h  106 (kg/m2s)

h/P  109 (kg/m2sPa)

0.24 0.27

2.42 2.41

5.17 5.15

4.20 4.54

0.24 0.22

2.45 2.31

5.23 4.93

2.90 3.03

4.71 4.69

0.21 0.21

1.20 1.15

5.13 4.92

57.8 55.0

0.82 0.86

5.84 5.88

0.17 0.17

2.75 2.60

2.33 2.20

0.76

60.2 58.0





0.11 0.12

1.32 1.27

2.82 2.71

0.76

28.2 27.1





0.12 0.12

0.62 0.59

2.65 2.52

J. M. P. Q. DELGADO

MBV (g/m2%RH)

Materials

ET AL.

291

Estimation of Moisture Buffer Performance 0.5

(a)

Gypsum plasterboard (65-85%, 20°C) - Initial cycle Gypsum plasterboard (65-85%, 20°C) - Stable cycle Plywood (33-75%, 23°C) - Initial cycle Plywood (33-75%, 23°C) - Stable cycle

t/(∆w/A)(m2h/g)

0.4

t/(∆w/A)=0.0277t+0.115

t/(∆w/A)=0.0308t+0.115

0.3

t/(∆w/A)=0.0182t+0.107

0.2 t/(∆w/A)=0.0173t+0.101

0.1

0.0 0

0.5

(b)

2

4

6 t (h)

8

10

12

10

12

Gypsum plaster (65-85%, 20°C) - Initial cycle Gypsum plaster (65-85%, 20°C) - Stable cycle

t/(∆w/A)(m2h/g)

0.4 t/(∆w/A)=0.0257t+0.121

0.3 t/(∆w/A)=0.0218t+0.114

0.2

0.1

0.0 0

2

4

6 t (h)

8

Figure 4. (a) Dependence of t/(w/A ) ¼ f(t), in the initial and stable cycles, for gypsum plasterboard and plywood specimens and (b) gypsum plaster specimen.

of the tests. This conclusion was confirmed with other building materials experiments presented in a previous work (Ramos and Freitas, 2004). The application of the sorption kinetics models to these experiments can lead us to the same conclusion; because the h value is reproduced from one test to the other with that same scale factor (Table 2). Extrapolation of Sorption Kinetic Curves The results of the experiments of sorption developed by Svennberg (2002) with a specimen of Scandinavian type of plasterboard for indoor use, plain

292

J. M. P. Q. DELGADO (a)

45

Gypsum plasterboard (65-85%, 20°C) - Initial cycle Gypsum plasterboard (65-85%, 20°C) - Stable cycle Plywood (33-75%, 23°C) - Initial cycle Plywood (33-75%, 23°C) - Stable cycle Eqs. (5) and (6)

40 35 ∆w/A (g/m2)

ET AL.

30 25 20 15 10 5 0 0

(b)

2

4

6

8

10

12 14 t (h)

16

18

20

22

24

18

20

22

24

40 Gypsum plaster (65-85%, 20°C) - Initial cycle Gypsum plaster (65-85%, 20°C) - Stable cycle Eqs. (5) and (6)

35

∆w/A (g/m2)

30 25 20 15 10 5 0 0

2

4

6

8

10

12 14 t (h)

16

Figure 5. (a) Mass variation observed, in the initial and stable cycles, for gypsum plasterboard and plywood specimens and (b) gypsum plaster specimen.

plasterboard (density 720 kg/m3, thickness 12.5 mm) were used, as example, for extrapolation of sorption kinetic curves. The experiments were performed during approximately 150 h with a RH step of 33–54% or 54–33%, and a constant temperature of 20 C. The increase/decrease in mass was continuously recorded for over 150 h and the results of plain plasterboard are plotted in Figure 8(b). Svennberg (2002) showed that the equilibrium water content shall be 14.5 g/m2. Figure 8(a) shows that the pseudo-second-order model fitted the experimental data very well, with weq ¼ 14.6 g/m2, t0.5 ¼ 1.78 h, and K2 ¼ 1.07  102 m2/kg s, for adsorption process, and weq ¼ 0.29 g/m2, t0.5 ¼ 3.27 h, and D2 ¼ 5.98  103 m2/kg s, for desorption process.

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Estimation of Moisture Buffer Performance 30

Cement plaster (65-85%, 20°C) - Initial cycle Cement plaster (65-85%, 20°C) - Stable cycle Equation (9) with n=5

∆w/A (g/m2)

25 20 15 10 5 0 0

2

4

6

8

10

12 14 t (h)

16

18

20

22

24

Figure 6. Mass variation of the cement plaster specimen during laboratory tests.

However, this experiment has a duration of 150 h, and it is possible, using the Ja¨ntti method, to calculate the asymptotic value of the adsorbed mass immediately after the beginning of the adsorption measurements. Using Equation (16), for the adsorption process, with t ¼ 1 h, t ¼ 2 h, and t ¼ 4 h, for example, the weq value, for 54% RH, obtained is constant and equal to weq ¼ 14.3 g/m2 (a value very similar to the one obtained by Svennberg, 2002). The parameter  calculated for infinitesimally small values of t, using Equation (18), is equal to  ¼ 1.83 h (very similar to t0.5 ¼ 1.78 h). Figure 8(b) shows that molecular adsorption mechanisms of plain plasterboard is well represented by, wðtÞ ¼ 14:3

t=1:83 1 þ t=1:83

ð19Þ

with the sorption kinetics coefficient equal to K2 ¼ 1=ð weq Þ ¼ 1:06  102 m2 =kg s (very similar to K2 ¼ 1:07  102 m2 =kg s, obtained with a pseudo-second-order model). DISCUSSION These experiments were carried out at the same time as a Nordtest project on moisture buffer capacity of building materials, so our version of what could be an MBV, although very close is not the official definition with test protocol proposed by Rode et al. (2005).

294

J. M. P. Q. DELGADO 1.0

(a)

Gypsum plaster (65-75%, 20°C) - Initial cycle Gypsum plaster (65-75%, 20°C) - Stable cycle

0.8 t/(∆w/A) (m2h/g)

ET AL.

t/(∆w/A)=0.0513t+0.241

0.6

0.4 t/(∆w/A)=0.0492t+0.232

0.2

0.0 0

30

(b)

4

6 t (h)

8

10

12

10

12

Cement plaster (65-85%, 20°C) - Initial cycle Cement plaster (65-85%, 20°C) - Stable cycle Cement plaster (65-75%, 20°C) - Initial cycle Cement plaster (65-75%, 20°C) - Stable cycle Equation (9) with n=5

25

∆w/A(g/m2)

2

20 15 10 5 0 0

2

4

6 t (h)

8

Figure 7. (a) Influence of different relative humidity amplitude in the initial and stable cycles of gypsum plaster specimen and (b) cement plaster specimen.

The MBV retrieved from these experiments can be an easy way of comparing different building materials or building elements in terms of their moisture buffer capacity. The properties that are usually applied in the characterization of the hygroscopic behavior of a material, such as vapor permeability and sorption curves, can be very useful for modeling, for instance, but it is not easy to use them as means for evaluation of the material’s performance under dynamic conditions. These properties are determined under static conditions, and they can not be easily combined into a simple number that could be used for comparison of different building systems or materials, especially when coatings are applied and the surface

295

Estimation of Moisture Buffer Performance 12

(a)

Plain plasterboard (33-54%, 20°C, Adsorption) Plain plasterboard (54-33%, 20°C, Desorption)

t/(∆w/A) (m2h/g)

10

Desorption t/(∆w/A)=0.0677t+0.213

8 6 4 2

Adsorption t/(∆w/A)=0.0685t+0.122

0 0

(b)

20

40

60

80 t (h)

100

120

140

160

16 14 w(t)=14.3

12

t/1.83 1+t/1.83

∆w/A (g/m2)

10 Plain plasterboard (33-54%, 20°C, Adsorption) Plain plasterboard (54-33%, 20°C, Desorption) Pseudo-second-order model Extrapolation of sorption kinetics curve

8 6 4 2 0 0

20

40

60

80 t (h)

100

120

140

160

Figure 8. (a) Dependence of t/(w/A ) ¼ f(t) by the plain plasterboard test specimen (Svennberg, 2002) and (b) the kinetics of adsorption and desorption.

resistance is not negligible. Instead, the MBV represents the amount of vapor that a system can retain in a cyclic load. The moisture buffer performance under dynamic behavior can therefore be expressed by a single number. As we look at the initial cycle and the stable cycle, also other aspects of the system behavior, such as hysteresis, are also implicit in that number. This work was meant to analyze the moisture buffer performance of materials, and we believe that the MBV experiments provided a good starting point. The sorption kinetics analyzes was the next step, as it can provide a better insight on moisture buffer performance.

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J. M. P. Q. DELGADO

ET AL.

Experimental data show that the step-response to a humidity step change can be divided into one initial rapid process followed by a slower concluding process. An advantage of the use of kinetics models for adsorption/ desorption processes is the possibility that the end of a sorption process, weq, may be predicted, using only a few hours experiment, with good agreement of the results. Also, the percentage of the final moisture content can be estimated for the considered time period. On the other hand, the MBV corresponding to an amount of moisture adsorbed in a predefined cycle, can be predicted from the knowledge of weq and kinetics coefficients. These can even come from static measurements if the hysteresis effect is not too relevant. But given the cycle definition (temperature, humidity step, and time step) it would be possible to anticipate any moisture uptake and not just the one attached to a specific cycle. As an example, we can think of MBV being defined for an 8–16 h high–low RH step as the definition proposed by the Nordtest project. This time step fits the normal use of a bedroom, with 8 h of daily moisture production. But if we want to evaluate the buffer performance on a room with a different time step, MBV would probably not correlate so well to the buffer performance of materials. With the knowledge of the kinetic parameters, a different MBV could therefore be anticipated, fitting the new operation conditions. It was possible to observe on Table 2 that, for the tested materials, the values of weq and K2 obtained in the initial and stable cycles are very similar, and the similarity of these two cycles increase in the value of initial sorption rate, h. This result was already expected, because the adjustment equation has two parameters and the experimental error is narrowed when the obtained values are multiplied. For our experiments the predicted constant mass at the end of the sorption procedure are, for example, weq ¼ 36.9 g/m2, for gypsum plasterboard and weq ¼ 45.7 g/m2, for gypsum plaster; which are very similar to the ones obtained with the specimens placed inside sealed glass vessels, at 85% RH provided by KCl. The specimens, initially at 65% RH, were weighed weekly until no change in specimen mass in consecutive weights indicated that equilibrium had been established, and equilibrium water content obtained were weq ¼ 39.0 g/m2 and weq ¼ 56.2 g/m2, for gypsum plasterboard and plaster, respectively. The specimens used in these tests had already been used in a previous work of Freitas (1999), with the same results for the maximum expected moisture adsorption for this variation of RH. The h value can be important because it reflects the initial buffer performance of the material. However, the results show that the materials with higher MBV may not be the ones with higher initial sorption rate (Table 2). This expected conclusion does not remove the importance

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of h value, because we obtained a measure that can be a precious help in the characterization of initial hygroscopic performance of different building materials. The study of complex building elements, starting with coated renderings, will also test the practical use of kinetic analysis compared to the use of MBV. CONCLUSIONS A description of results from experimental investigations on gypsum plaster, gypsum plasterboard, cement plaster, and plywood exposed to cyclic step changes in RH, at constant temperature, is presented. The results obtained were analyzed in terms of moisture buffer value (MBV) and kinetics parameters. The MBV as it was proposed by Rode et al. (2005) can be a way of evaluating the moisture buffer performance of building materials or systems. The laboratory tests showed that the material’s velocity when reaching for equilibrium with the environment can be translated with parameters specific of that material. The knowledge of the parameters that define the kinetic behavior of a material or system enables us to predict the cyclic moisture uptake of a material, given the step definition responsible for it. This allows for a prediction of MBV (associated with 8–16 h 75–33 RH step) or a similar value adapted to different step changes. As to the kinetic parameters, themselves, it is not easy to use them in the same way as MBV. It was clear that h indicates the buffering potential for initial stages. But it is not possible to retrieve a kinetic parameter that would have the same interpretation of MBV. Future work shall look at the application of kinetics on systems instead of materials, and advantages of that shall be discussed. NOMENCLATURE A ¼ area (m2) D1 ¼ pseudo-first-order rate constant of desorption (s-1) D2 ¼ pseudo-second-order rate constant of desorption (m2/(kg s)) h ¼ initial sorption rate (kg/(m2 s)) K ¼ kinetic coefficient (h1) K1 ¼ pseudo-first-order rate constant of sorption (s1) K2 ¼ pseudo-second-order rate constant of sorption (m2/kgs) MBV ¼ moisture buffer value (g/(m2%RH)) n ¼ order of sorption kinetic equations

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ET AL.

P ¼ pressure (Pa) t ¼ time (h) t0.5 ¼ time to reach 50% of equilibrium water content (h) T ¼ temperature ( C) w ¼ water content (g/m2) wi ¼ initial water content (g/m2) weq ¼ equilibrium water content (g/m2)  ¼ angle (rad)  ¼ density (kg/m3)  ¼ characteristic time (h)

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