Oxygen and Water Vapor Transport Through Polymeric Film

Chapter 18

Oxygen and Water Vapor Transport Through Polymeric Film

Downloaded by MONASH UNIV on May 3, 2013 | http://pubs.acs.org Publication Date: March 9, 1988 | doi: 10.1021/bk-1988-0365.ch018

A Review of Modeling Approaches Roy

R. Chao and Syed S. H. Rizvi

Institute of Food Science, Food Science Department, Cornell University, Stocking Hall, Ithaca, NY 14853-7201 The dramatic growth in the use of polymeric films for food packaging asserts their many inherent advantages over other materials. However, during storage, such undesirable transport phenomena as permeation of moisture, oxygen and organic vapors through the polymeric film do occur and their knowledge and control become critical. These transport processes are affected by the thermodynamic compatibility between the polymer and the penetrant and the structural and morphological characteristics of the polymeric material. In this review, some modeling approaches for describing the transport of oxygen and/or water vapor through hydrophobic or hydrophilic polymeric films i n terms of variables generally evaluated for the film and the environmental conditions established within the package during storage are discussed and analyzed.

Prolonging the consumer-acceptable shelf life of food products i s the major benefit bestowed by the use of packaging. The first step in defining packaging requirements is quantifying the transport properties and the critical vectors of quality loss as well as the variables that influence them (1). The importance of transport behavior of gases and vapors i n polymeric films has become apparent with the accelerating development of highly impermeable or selectively permeable packaging films for diverse applications i n the food and pharmaceutical industries. Usually, films or coatings used for packaging foods are expected to resist transfer of moisture and non-condensable gases l i k e O2 and CO2, sorption of fats/oils and migration of additives.

0097-6156/88/0365-0217$06.75/0 © 1988 American Chemical Society

In Food and Packaging Interactions; Hotchkiss, J.; ACS Symposium Series; American Chemical Society: Washington, DC, 1988.


218

FOOD AND PACKAGING INTERACTIONS

I n same instances, however, regulated t r a n s f e r o f some o f them may be d e s i r a b l e . Other required f u n c t i o n a l properties o f f i l m s include: p r o t e c t i o n against mechanical hazards during transportation, s t r u c t u r a l and s a n i t a r y i n t e g r i t y , r e t e n t i o n of v o l a t i l e f l a v o r compounds and enhancement o f s a l e s appeal (2-3). P r e d i c t i o n of s h e l f l i f e , maximization o f economic b e n e f i t and regulatory considerations generally d i c t a t e the p r o p e r t i e s o f packaging materials, and transport properties i n p a r t i c u l a r , must be s p e c i f i e d . Therefore, development of models d e s c r i b i n g accurately the s p e c i f i c transport of gases and vapors through the f i l m s would be h i g h l y desirable. Many extensive reviews p e r t a i n i n g t o modeling o f permeation of gases and vapors i n polymeric materials have been reported i n the l i t e r a t u r e (4-20) ; and over 7,000 apparently relevant and p e r i p h e r a l papers i n the past two decades are a v a i l a b l e i n the Chemical Abstract database (21). This review i s , therefore, concerned only w i t h aspects o f the s o l u t i o n and d i f f u s i o n o f oxygen and water vapor through polymeric materials. A t t e n t i o n has been d i r e c t e d s p e c i f i c a l l y a t fundamental understanding of the processes and approaches taken t o quantify them. General Theory of Permeation There are u s u a l l y two types o f mechanisms o f mass t r a n s f e r f o r gases and vapors permeating through packaging m a t e r i a l s ; namely, a c a p i l l a r y flow type and an a c t i v a t e d d i f f u s i o n type (22). C a p i l l a r y flow involves small molecules permeating through pinholes and/or h i g h l y porous media such as paper, g l a s s ine, c e l l u l o s i c membranes, e t c . Activated d i f f u s i o n c o n s i s t s of s o l u b i l i z a t i o n o f the penetrants i n t o an e f f e c t i v e l y non-porous f i l m a t the i n f l o w (upstream) surface, d i f f u s i o n through the f i l m under a concentration gradient and release from the outflow (downstream) surface a t the lower concentration. I n f l e x i b l e packages o f e i t h e r h i g h l y porous media o r w i t h gross defects such as cracks, f o l d s , and pinholes, the dominant mechanism i s c a p i l l a r y flow which a c t u a l l y determines the transmission rates. The flow r a t e o f a penetrant i n such cases depends on the s i z e o f the c a p i l l a r i e s , s i z e and v i s c o s i t y o f the penetrant, and both the t o t a l pressure and pressure d i f f e r e n t i a l across the f i l m . I n the case o f non-porous polymeric f i l m s , the mass transport o f a penetrant b a s i c a l l y includes three steps: adsorption, d i f f u s i o n , and desorption. Adsorption and desorption depend upon the s o l u b i l i t y o f the penetrant i n the f i l m , i . e . the thermodynamic c o m p a t i b i l i t y between the polymer and the penetrant. D i f f u s i o n i s the process by which mass i s transported from one p a r t o f a system t o another as a r e s u l t of random molecular motions. Within the polymer matrix, the process i s viewed as a s e r i e s o f a c t i v a t e d jumps from one vaguely defined " c a v i t y " t o another. Q u a l i t a t i v e l y , the d i f f u s i o n r a t e increases w i t h the increase o f the number o r s i z e o f c a v i t i e s caused by the presence of substances such as p l a s t i c i z e r s . On the other hand, s t r u c t u r a l e n t i t i e s such as c r o s s l i n k s o r degree o f c r y s t a l l i n i t y decrease the s i z e o r number o f c a v i t i e s and thereby decrease the d i f f u s i o n rate.


18. CHAO & RIZVI

Ο and RJD Vapor Transport

219

The migration of the penetrant i n a polymeric f i l m can a l s o be v i s u a l i z e d as a sequence of u n i t d i f f u s i o n steps o r jumps during which the p a r t i c l e passes over a p o t e n t i a l b a r r i e r separating one p o s i t i o n from the next. The d i f f u s i o n process requires a l o c a l i z a t i o n of energy t o be a v a i l a b l e t o the d i f f u s i n g molecule and i t s polymer chain segment neighbors. T h e o r e t i c a l l y , the l o c a l i z a t i o n of energy provides what i s needed f o r rearrangement against the cohesive forces o f the polymeric medium w i t h e f f e c t i v e movement of the penetrant f o r a successful jump. A more thorough d i s c u s s i o n on the d i f f u s i o n process i s provided by Roger (21).


Permeability and Related Equations A t constant temperature and d i f f e r e n t i a l p a r t i a l pressure, d i f f u s i o n of a penetrant through a polymeric f i l m of u n i t area normal t o the d i r e c t i o n of flow f o r a p e r i o d of time leads t o a steady s t a t e of d i f f u s i v e f l u x , J ,

(1)

J = Q/At

where Q i s the t o t a l amount of penetrant which has passed through surface area A i n time t . F i c k ' s f i r s t law of d i f f u s i o n a l s o applies: J

=

- Ό(δο/δχ)

(2)

where χ i s the space coordinate normal t o the reference p l a c e ; c i s the concentration of the d i f f u s i n g penetrant; and D, i s the d i f f u s i v i t y , assumed independent of x, t , o r c. For experimental and p r e d i c t i v e purposes, the d i f f u s i n g concentration, c, i s u s u a l l y r e l a t e d t o the ambient penetrant concentration, C, i n contact w i t h the polymer surface by the Nernst d i s t r i b u t i o n function c = KC

(3)

where Κ i s the d i s t r i b u t i o n c o e f f i c i e n t and i s a f u n c t i o n o f temperature. Often, penetrant concentration, c, i s a l s o proportional t o pressure, p, through an appropriate gas law equation. For example, when Henry's law i s obeyed (c = pS), i t follows t h a t the steady s t a t e f l u x can be w r i t t e n as J = DS(

P l

- p )/L

(4)

2

where p i and P2 are the respective upstream and downstream pressure of the f i l m of thickness L, and S i s the Henry's law s o l u b i l i t y c o e f f i c i e n t , assumed independent of ρ and c. By d e f i n i n g the permeability constant, P , as the product o f s o l u b i l i t y and d i f f u s i v i t y , Equation 4 i s used f o r evaluating the permeability constant, m


220

FOOD AND PACKAGING INTERACTIONS 1

L « Q P =

DS =

m

(5) A ·t

(P! - p ) 2

This i s the b a s i c equation f o r deterndning the permeability constant. However, D and S generally vary w i t h c, p, x, o r , t so t h a t P w i l l a l s o be dependent on those v a r i a b l e s . Experimental methods and apparatus f o r the measurement o f S, D, and P have been described by many i n v e s t i g a t o r s . Current commercial gas and vapor transmission iristruments include the ASIM (American Society f o r Testing Materials) standard t e s t Dow-Park c e l l , the Linde c e l l , c e l l s f o r use w i t h a mass spectrometer detector, various water vapor transmission c e l l s and t h e Mocon iristruments f o r 00 , 0 , and water (19). These instruments are adequate f o r the determination o f permeability a t steady-state. Commercially a v a i l a b l e micxobalances are used t o measure r a t e s o f s o r p t i o n and desorption. Other systems using volumetric, o p t i c a l r a d i o t r a c e r , weighing cup and a v a r i e t y o f other measurement methods has a l s o been described (19). m

m


2

2

Unsteady State D i f f u s i o n Measurements When a penetrant d i f f u s e s through a polymeric f i l m i n which i t i s soluble, there i s a t r a n s i e n t s t a t e before the steady s t a t e i s established. Two approaches are used t o quantify t h e unsteady s t a t e process. I n t e g r a l Permeation Method I n t h i s technique, the penetrant pressure ρχ a t the upstream face o f the polymer i s generally h e l d constant. Meanwhile, the downstream pressure, p , w h i l e measurable, i s n e g l i g i b l e r e l a t i v e t o the upstream pressure. When Henry's law i s a p p l i c a b l e , a t y p i c a l p l o t o f gas transmission versus time appears as shown i n Figure 1. The i n t e r c e p t on the time a x i s o f the extrapolated l i n e a r steady s t a t e p o r t i o n o f the curve, r, i s known as the "time l a g " and can be expressed as (23) 2

2

r = L /6D

(6)

Therefore, a l l three parameters - P from the steady s t a t e p o r t i o n o f the curve, D from the time l a g , and S from P^/D - can be determined from the s i n g l e experiment by analyzing steady and non-steady flow through a membrane (24). S o l u b i l i t y constants determined by the time-lag method, however, are l e s s p r e c i s e f o r more s o l u b l e gases, e.g. carbon dioxide, ethane, e t c . , than those determined by the equilibrium-sorption method. The p r e c i s i o n l i m i t s on s o l u b i l i t y constant by the time-lag method are estimated a t 10 ± 1.0% (25). For a penetrant-independent d i f f u s i v i t y , the steady-state flow through a plane sheet i s approximately reached a f t e r a p e r i o d amounting t o 2.7 r (16). I f the d i f f u s i v i t y , D, i s not constant, but depends upon c, then a mean value o f the d i f f u s i v i t y , D, may be defined as m


18. CHAO & RIZVI

Ο and H 0

D = (1/Ci)

221

Vapor Transport

?

(7)

D(c)d

0


where i s the penetrant concentration a t the upstream penetrant membrane surface. Generally, as long as the upstream concentration does not exceed roughly 10 wt. percent o f the polymer, the d i f f u s i v i t y can be described by the f o l l o w i n g equation D(C) = D exp(Gc)

(8)

Q

where D i s the value o f D(c) a t zero d i f f u s i n g component concentration; G i s a " p l a s t i c i z i n g parameter" t h a t can be r e l a t e d to the Flory-Huggins polymer-solvent i n t e r a c t i o n parameter (12,26). I t has been shown (27) t h a t the f o l l o w i n g i n e q u a l i t y holds f o r a l a r g e c l a s s o f fundamental dependencies o f D on penetrant concentration Q

2

1/6

Oxygen and Water Vapor Transport Through Polymeric Film

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